Small Stella Manual
Last updated 29th March 2020.
The latest version of this manual can be found online at
https://www.software3d.com/StellaManual.php?prod=Small
This manual contains instructions to get you started using Small Stella.
It covers most features, and after reading this document you should be able to
find your way around most of the interface.
If you get stuck, feel free to ask questions on the Stella forums at
http://www.software3d.com/Forums.
Or follow Stella on facebook at
http://www.facebook.com/Stella4D.
The program includes Platonic, Archimedean, Kepler-Poinsot and Johnson solids,
some Stewart toroids, compounds, and other models.
The default window layout has two views side-by-side, showing the
base polyhedron on the left and its net (or one of its nets) on the
right. The default base model is the icosahedron.
Use the Right and Left arrow keys to change to the
next/previous model in the built-in list (or the menu items
"Poly→Next Polyhedron" and
"Poly→Previous Polyhedron", or the green left and right arrow
buttons on the main toolbar or at the top of some views). Note: if
you have loaded a .stel file, then the arrow keys move forward and
backward through files in the same folder instead. Furthermore, the arrow
keys, unlike the green arrow buttons and menu items, are context
sensitive. That is, they behave differently depending on what type of view
is currently active. If the current view has yellow arrow buttons at the
top, then they performs the function of those instead (e.g. changing to the
previous/next net if the unfolded net view is active). See more about yellow
arrow buttons later. You can also use Ctrl+Left and
Ctrl+Right to go to the previous/next model, regardless of the
selected view (they behave exactly like the green arrow buttons).
The built-in list is divided into a hierarchy of categories. You will see
the current category and model name displayed in the main toolbar. Clicking on
either of these names opens a list of other categories or models to choose
from, providing a more direct way to select a model.
The categories are as follows:
- Search Results: List of search results.
See searching below.
- All Built-in Polyhedra: All the models below in one long list.
- Uniform: All uniform polyhedra.
- Regular: All regular polyhedra.
- Platonic: The five convex regular polyhedra.
- Kepler-Poinsot: The four nonconvex regular polyhedra.
- Semi-Regular: All semi-regular polyhedra.
- Archimedean: The 13 convex uniform (but not regular)
polyhedra. There's no category for their duals,
the Catalan solids, because the dual of any polyhedron is
instantly available in Small Stella already. So access them via this
list.
- Prisms/Antiprisms: Convex uniform polyhedra with dihedral
symmetry. Includes prisms and antiprisms.
- Johnson Solids: The 92 remaining convex regular-faced polyhedra.
- Near Misses: Some models that are "almost" Johnson solids. In each
case some of the faces are not quite regular.
- Stewart Toroids: Regular-faced polyhedra with genus greater than
zero, i.e. with holes. Most are not self-intersecting. A few regular-faced
polyhedra with genus zero are included. Stewart used these as building blocks
for some of his toroidal models. See Stewart's book
Adventures Among the Toroids for more information.
- Stella Library: This category contains extra models that are
not actually built into the program, but rather come from an additional library
of models provided with Small Stella. These reside in a folder called
"SmallStellaLib" under the folder where Small Stella is installed.
You can add your own .stel files to the folder and they will also
appear in this category. The library includes some popular compounds (5 cubes,
5 octahedra, 2/5/10 tetrahedra) and a collection of geodesic domes and spheres.
- Geomag Library: This category contains fun models which can be made
using Geomag's construction kit. These reside in a
folder called "GeomagLib" under the folder where Small Stella is
installed.
You can add your own .stel files to the folder and they will also
appear in this category.
Another way to find a polyhedron is to use
"File→Polyhedron List...", hit Ctrl+N, or click the
matching button on the main toolbar. This opens a window listing all the
polyhedra provided. A list of categories on the left, and a list of polyhedra
from the current category on the right. The list of polyhedra has several
columns, including the primary symbol, name, and the number of faces, edges,
and vertices. The list may be sorted according to any column by clicking on
the header of that column. Click a second time to reverse the order. To
return to the original order, click on the header of the first column.
Select a category on the left, then select a polyhedron on the right.
Information about the selection appears at the bottom, including other common
names, dual names, Wythoff symbol, Wenninger number and page number in
Wenninger's books Polyhedron Models and Dual Models where the
model can be found. Click OK or hit Enter to open the selected
polyhedron.
Rather than looking through the list, you can enter a symbol or name
directly in the Search field at the top. Symbols for uniform polyhedra
may be any of the following:
- Vertex descriptions (separated by either commas or dots). E.g.
"4.4.4" (cube)
or "(3.3.3.3.3)/2" (great icosahedron).
- Wythoff symbols. E.g. "3 | 2 4" (cube)
or "5/2 | 2 3" (great icosahedron).
- Index in Magnus Wenninger's book Polyhedron Models, entered with a
"W" prefix. E.g. "W3" (cube)
or "W41" (great icosahedron).
- Index from Roman Maeder's list at
http://www.mathconsult.ch/showroom/unipoly/list.html,
entered with a "U" prefix (or "M"). E.g. "U6" (cube)
or "M53" (great icosahedron).
- Index from Zvi Har'El's Kaleido program, entered with a "K" prefix.
E.g. "K11" (cube)
or "K58" (great icosahedron).
Other models use different notations. For example, enter "J4" for the
square cupola, one of the Johnson solids. This provides a very quick way to
jump to a particular Johnson solid if you know its number.
You may also enter the name of a polyhedron. It can be either the full
name (including known alternative names and dual names), a substring in the
name, or an abbreviation for the name using either the first letter from each
word, or the first letter from each part of each word. Some examples:
- "Cube". Case is ignored, so "cube" or "CUBE" will also work.
- "T", "O", "C", "I", "D". Abbreviations for the Platonic solids:
tetrahedron, octahedron, cube, icosahedron and
dodecahedron.
- "CO". Abbreviation for cuboctahedron.
- "RTC". Abbreviation for rhombic triacontahedron.
Since this is the dual of a built-in model, rather than being a built-in model
itself, the icosidodecahedron is the model that will be loaded, but you can see
the RTC in the dual view, and will be prompted to switch to a dual view if you
don't have one open already.
As you type into the search field, you'll notice it finding the best match as
you go. Hit Enter to load a model as soon as it finds the one you're
after.
Below the search field is a choice between Find one and Find
all. So far we've been using the default, Find one, which means the
first match is found. Find all finds all matches, and lists them in the
special Search Results category at the top of the category list. Select
an item from the list and open it. Now you can use the Left and
Right arrow keys (or green arrow buttons) to step through the search
results.
To the right of the big Search field are some smaller fields where
you can enter
face, edge and vertex counts. If you enter a number, this also becomes part of
the search. For example, enter "12" in faces, and only polyhedra with 12 faces
will be found. A range may be entered, such as "12-24", to find all polyhedra
with between 12 and 24 faces. You may enter values into more than one field to
further narrow the search. Comprehensive tooltips help explain how to use each
field, so hover the mouse them to find out more.
With the Search Results category and Find all selected,
another button appears labelled ←Locate search result. Click this
to locate the selected polyhedron in its original category.
Every polyhedron has a dual, which won't be explained fully here, but
you may think of it as the model's opposite. It has the number of faces
and vertices swapped with respect to the original model, and the same number of
edges. The dual of the dual brings us back to the original model again.
Hit "d" to switch between the base polyhedron and its dual. The
net will also change.
At any point you may save a model you like to Small Stella's native format,
the .stel file. Everything about your scene is saved here, including
your current screen layout and views, the model itself,
various settings, and the state of mouse inertia. The
latter means that if your model is spinning, morphing or folding etc. when you
save it, then it will be spinning, morphing or folding again when you reload
it.
Use "File→Save" or "File→Save As" to save your
model, and "File→Open" to re-open it later. In the file browser
that appears, select an existing .stel file to see some information
about it in the preview area at the bottom of the browser. You will see the
number of faces, edges and vertices, and the first line of the comment field
from the Info Window if one has been set.
Tip: Any .stel files saved from Small Stella before version 5.0 will
need to be loaded and re-saved in order to support this information preview in
the browser.
If you particularly like a model, you may make it load immediately when
Small Stella starts up by using "File→Save Default Scene". Next
time you start Small Stella, this model will load automatically. You may even
use this just to set up your view layout the way you like
it.
The mouse does many different things, depending on what mode you're in,
which view you're in, whether you're holding down the left/right/both mouse
buttons, and whether you're holding down Shift/Ctrl/Neither/Both/Space. Watch
for the tips in the bottom right hand corner, which show you what the mouse
buttons do in the current situation. The tips change when you hold down
Shift/Ctrl/Neither/Both/Space. They may also change when you move the pointer
from one view to another. Even I forget what the mouse can do in some modes,
so these on-screen tips help a lot!
Sometimes just clicking is required (e.g. Shift+Left-click
to select a face). Sometimes dragging in 2D is required (e.g.
Left-Drag to tumble the polyhedron). And sometimes dragging in 1D is
required (e.g. Right-Drag to zoom in/out).
All basic navigation is done with the mouse and no need to touch the
keyboard, except for some less common movements. These mouse controls
generally continue to work in different modes too.
In a 3D view:
- Left-drag: tumble/rotate
- Right-drag: zoom in or out
- Left+Right-drag or Middle-drag: twist
(rotate around the viewing axis). Left+Right-drag means to hold down both the
left and right mouse buttons while moving the mouse. Any time
Left+Right can be used in Small Stella, you may use the
Middle button instead, if your mouse has one.
Tumbling and twisting both have mouse inertia, so
you can release the mouse buttons while dragging and the model will continue to
tumble or twist. To stop it, perform the same action again, but clicking
instead of dragging the mouse (e.g. do Left-click to stop tumbling).
You may also hit Esc to stop any mouse inertia.
Similarly in a 2D view:
- Left-drag: pan sideways
- Right-drag: zoom in or out
- Left+Right-drag: twist (rotate)
With 2D views, zooming zooms in on the point where the mouse was when you first
clicked the right button, so you can zoom in on a specific point. As with 3D
views, twisting has mouse inertia.
A couple of more advanced navigation controls are available in 3D views.
Hold down the Space bar and you'll notice the mouse-tips in the bottom
right corner change:
- Space+Left-drag: move sideways
- Space+Right-drag: change field-of-view. This affects how
strong the perspective effect is.
- Space+Left+Right-drag: pivot around an axis. Select a
face, edge, vertex, or rotational symmetry axis (see
Symmetries), and this operation will pivot around an
axis through that selected item. You may deselect the item and the axis will
be remembered (until another item is selected).
If you find that you want to pivot around a selected axis more often than
twisting, select "Options→Right-drag to Pivot Around Selected
Item" (or matching toolbar button). This swaps the operations of
Right-drag and Space+Right-drag.
You may also switch each view between perspective and orthogonal projections
by ticking/unticking "View→Orthogonal View" (keyboard shortcut:
O). Perspective views are what we see in the real world, where things
closer to the camera appear to be larger. Orthogonal views are like
architectural plans, where distance from the camera does not affect the
apparent size of objects.
Finally, you can use items on the "View→Camera" submenu to
store and recall camera positions. The field-of-view and
perspective/orthogonal setting are also stored.
The faces of polyhedra may be exploded apart as follows:
- Ctrl+Shift+Left-drag: Drag to explode faces apart or
together.
- Ctrl+Shift+Right-click: Unexplode faces, bringing them back
to where they started.
This can be useful for examining the internal structure of faces that would
otherwise be partly or entirely hidden.
Exploding has inertia, so if you release the mouse
button while still dragging, the exploding will continue at the current rate.
It will remember how far apart the faces are and use this as one extreme in the
explosion. So faces will explode out to this point, then turn around and
implode again. The other extreme, at the imploded end, is determined by the
following menu item:
- Options→Allow Explosion Inertia to Implode. When ticked, faces
will implode back through each other and out the other side, to the same
distance as the extreme in the other direction. When not ticked, faces will
only implode back to their original positions before changing direction and
exploding again.
Exploding faces is available in most 3D views, but not the Unfolding Net view.
You can hit Esc to cancel all sorts of things. It performs the
first appropriate action on the list below.
- Skip transition
- Stop playing a tour
- Stop all mouse inertia. This is very handy when
things are spinning and morphing and folding and exploding and you can't
remember what combination of Shift, Ctrl, Space, and
Left and/or Right mouse buttons you used to start all that
happening!
- Exit any mode back to normal mode
- Exit full-screen display
- Exit 3D stereoscopic display
In the default mouse selection mode (see below),
faces, edges and vertices may be selected with the mouse.
- Shift+Left-click or double Left-click:
Select a face, edge, vertex, or symmetry axis. The selected item is
highlighted in white and will partly show through other faces (try rotating the
model so that the item is on the other side). Only one item may be selected at
a time. Many operations work on the current item, which is either the
selected item, or the most recently selected face if no item is selected. If a
face has not yet been selected, then the first face is the current face.
- Ctrl+Left-click: Select only faces (not an edge or vertex).
- Ctrl+Right-click: Select only edges.
- Shift+Right-click or double Right-click:
Select only vertices. A selected vertex is highlighted with a white dot, and
half of each surrounding edge is also highlighted. This also selects the
corresponding face of the dual, which will also become
highlighted if you have a dual view open.
Selecting a vertex is useful in a few situations, such as when you have a
vertex figure view open and want to choose which vertex figure to look
at.
Face, edge and vertex types can also be selected via the
Info window.
Tip: When an edge is selected, its length is shown on the status bar at
the bottom of the window.
There are five toolbars arranged in three rows, with two in the first and last
rows by default. They may be dragged and docked to different sides of the
window, or dragged away into a separate window. Their positions will be
remembered between sessions. The toolbars are:
- Main toolbar: the top toolbar. Provides buttons for file
opening/saving, selecting polyhedra from the built-in list, and printing.
- Tour toolbar: to the right of the main toolbar. Contains buttons
for loading, saving and creating tours, which are like animated
slideshows of polyhedra. See Tours.
- Options toolbar: below the main toolbar. Provides buttons for
various options and operations.
- Mode toolbar: left-hand toolbar under the options toolbar.
Contains buttons for changing the current mouse-selection mode,
which affects what the mouse does when holding down Shift and/or
Ctrl and clicking a mouse button. Normal navigation with the mouse
remains unchanged. Exactly one of these buttons will be pushed in at any time,
indicating the current mode. A helpful message appears when entering any mode
other than the default mode, and don't forget to keep an eye on the mouse tips
in the bottom right corner of the main window to see what the mouse does. You
can hit Esc to return to the default mode. See
Mouse Selection Modes for more information about modes.
- View toolbar: right-hand toolbar under the options toolbar.
Contains buttons that change the current view to a different type. Exactly
one of the buttons on the view toolbar will be pushed in at any one time,
indicating the current view type. Try clicking through the different buttons
to see all the different kinds of view.
The buttons all have tool-tips, so if you place the mouse over a button
and don't move for a moment, a small description of the button appears.
In addition, there are further buttons in the top right corner of each view.
The buttons that appear depend on the type of view. Yellow left or right
arrow buttons are for changing to the previous or next item that this view type
can display. For example, in the 2D net view, these buttons cycle through the
various nets required. If the current view has yellow arrow buttons, then you
can use the left and right arrow keys on the keyboard to perform the same
function.
The Info window is a special window for displaying information about
the current polyhedron. There are three ways to open or close it: via the
"View→Model Info" menu item; via the equivalent button on the
options toolbar; or by simply hitting "i" on the keyboard.
Information includes number of faces, vertices and edges, number of edges
that must be cut/folded/glued to make the model, alternative names for the
model (if any) and lots of other info. It is presented in a tree structure,
where collections of similar data are grouped together. A small "+" or "-"
sign beside each item may be clicked with the mouse, allowing each section
to be expanded to show all the data in that group, or collapsed
to hide the data. Which groups are expanded or collapsed is remembered between
sessions, so the data presented will always be the data of most interest to
you.
You can Right-click on information that may be edited to edit that
item. Most items can't be edited, but ones that can include the model's name,
the dual's name, comments about the model, internet link associated with the
model, radius, surface area and volume.
Expand the face, edge or vertex counts to see a list of face, edge or vertex
types. You can Left-click on a type to select a face, edge or vertex
of that type in the main view. Similarly, when a face, edge or vertex is
selected another way, the matching entry in the Info window will be
highlighted.
The Info window also shows how many parts belong to this compound (or "1" if
not a compound). Expand this item to see a list of the polyhedra in this
compound. Left-click on one to select a face belonging to that part.
This window starts off docked to the right hand side of the main window, but
like the toolbars, it may be dragged to dock elsewhere in the main window, or
dragged away into a free-floating window of its own. The position is
remembered between sessions.
By default there are two views, one showing the base polyhedron, and one
showing its net. You may choose a different layout with
"View→Choose Layout", or more conveniently by using
Ctrl+1 to Ctrl+6, depending on how many views you want. For
example Ctrl+4 will give you a four-view layout. Repeatedly hitting
Ctrl+4 will cycle through all the different four-view layouts
available.
Once you have the layout you want you can choose what kind of views are
shown by selecting each view in turn (by clicking in them or on their title
bars) and hitting one of the buttons on the view toolbar (or choosing from the
bottom section of the View menu).
Tip: To see which view is selected, look for the one with the
highlighted title bar. There's always exactly one selected view.
When you save a .stel file
(not available in the demo)
your layout and view types are also saved, and restored when the file is
opened another time. If you wish to open a file without changing the current
view layout, use "Options→Keep Layout when Opening Files". Once
ticked, you may continue to open further files without the layout being
affected.
There are eight types of view which show smooth morphing between a
polyhedron (or compound) and its dual.
Select one of these view types from the view toolbar, or from the
"View→View Duals Morphing" submenu. Use Ctrl+Left-Drag
to morph between the base and dual in these views. There's also mouse
inertia on this function, so you can release the mouse button while
dragging and the morphing will continue on its own.
Note: the demo version will not allow morphing for certain models.
This morphing may not act perfectly between all pairs of models. Some
methods cause parts to get flatter and flatter until they disappear, which
produces a visual jump, but isn't really wrong.
Another type of view is the Unfolded Net view. Use PageUp and
PageDown to move through the list of nets required. Hit Ctrl+P to
print the net (or to print any other view type, but make sure you have the
appropriate view selected first!).
The demo version will only allow you to print nets for the five Platonic
solids, but it will still let you see a print-preview of nets for any model.
The Net view shows one unfolded net at a time, but when printing, all required
nets are included. Small Stella attempts to pack as many onto each page as
it can to minimize paper requirements.
Printing must always be done via a print-preview, to avoid any issues with
unexpected settings. A dialog box appears first full of options for printing
nets, but you can ignore most of these to start with and just click on
"Preview" (or hit Enter).
If you're not sure about how to put the nets together, then look for the
"Edge connection IDs" tick-box in the dialog box that appears when
you print nets. Ticking this will cause numbers to be displayed beside each
edge around the net. Each number will appear exactly twice among all the nets.
Find the matching numbers to see which edges should be glued together. This is
especially useful for models with asymmetric color schemes, where the nets may
go together in various ways, but only one has the correct colors.
When printing, if the sale of the model is too big for nets to fit on your
printer's paper size, an error is given, with an offer to scale the model down
just enough so that the nets fit. The message also shows the factor by which
the model would be scaled down.
See Scale for details about printing nets in different
sizes.
The Folding Net view shows the nets in 3D, folding up into the final model and
unfolding again into separate flat nets. Use Ctrl+Left-drag to
interactively fold and unfold the nets. Mouse inertia applies here too,
so if you release the left mouse button while still moving the mouse, the
folding/unfolding will continue on its own at the current rate.
When unfolding, first the folded nets move apart from each other (if there's
more than one net), then they each unfold individually.
Ctrl+Right-click jumps to the point between these two stages, or just
folds the net half-way if there is only a single net.
The "Nets→Nets Shown in 3D View" submenu gives you control
over what is shown in the Folding Net view. Your options are:
- Show All Nets
- Show One Type of Net
- Show One Net
If you want to try something more unusual, try creating the
convex hull of a partly folded net using
"Poly→Create Convex Hull" with the Folding net view selected!
You may want to print all nets onto white paper, perhaps using a color printer
to fill in the face colors or images, or you may want to
print nets of different colors separately in order to print directly onto
colored paper (my usual technique).
The "Nets→Net/Paper Color Mixing" submenu allows this.
It contains the following options:
- Auto: Automatically choose between the two options below. Mixed
colors are used when the model is convex or has images on its faces. Otherwise
only a single color is permitted per net.
- One Color per Net/Page: Only allow faces of a single color in each
net and on each page of paper when printing. Use this when printing onto
colored paper, as I usually do.
- Allow Mixing of Colors: Faces of different colors may be combined
into single nets and printed onto the same pages. Use this if you want to use
white paper and a color printer to fill in the faces.
When mixing of colors is not permitted within nets, only nets of a single
color will be printed at any one time. For example, if there are red, yellow,
and blue parts, then you will need to do three print-outs to print all the
nets, one for each color. If you are currently viewing a yellow net in the
Unfolded Net View, then by default, printing will only print yellow nets, but
the dialog box has a drop-down list for choosing the paper color you want. For
the chosen color, all nets of that color will be printed, not just the one you
are viewing, and it will try to pack them together as best it can. The
print-preview lets you see how many pages are required, so you just put that
many pieces of red, yellow or blue paper in the printer tray (use manual feed
for thicker paper and to reduce curling on some printers).
In order to glue parts together when building a paper model, tabs are
usually left on some or all edges around each net. The following construction
methods are common:
- No-tab method. Don't use tabs at all. Parts may be connected with
tape or similar. I don't recommend this method for paper models. Tape is ugly
and deteriorates over time.
- Single-tab method. For each pair of edges to be glued together,
only one has a tab. It is glued directly under the part being attached.
- Double-tab method. Tabs are left on all edges around each
net. When parts are attached, it is their tabs that are glued together,
forming a kind of ribbing inside the model.
Most people seem familiar with the single-tab method, and indeed it's how I
first started, but for the most part I recommend the double-tab method for the
following reasons:
- Construction is easier. If using tweezers to squash the two tabs together
when gluing, it's generally easier to access them. With a single tab glued
under the connecting face, other parts of the model may get in the way.
- I think the result generally looks better, more precise.
- Gluing directly under a face that will be visible from outside can cause
problems. Sometimes the water in the glue can cause wrinkling. It also
matters more if you make a mess with the glue. Glue may get on the tweezers
or your fingers and be spread onto the face when squashed together with the
tab.
- It's also generally easier to put the last piece in! With double-tabs,
the tabs fold at half the dihedral angle as compared with single-tabs, so they
have more spring in them.
The single-tab method can still be useful in the following cases:
- When the angle between faces is very small, a single-tab can produce a
sharper result.
- When there's not enough room in the net for two tabs (though in this case
you may want to think about rearranging the net).
You may mix and match methods within one model. In such cases I would start
by attaching the single-tabs, which are harder to glue once more of the model
takes form.
Small Stella supports all three methods, or a mix of them. Tabs are
shown in both the Unfolded and Folding Net views. Use the
"Nets→Tabs" submenu to state your preference. With an edge
selected, the preference applies to that edge only. With no edge selected, you
will be setting the default preference. It contains the
following options:
- Use Default. Only available when an edge is selected. Tells the
edge to use the default setting. Other options below would tell it to override
the default.
- No Tabs. No tabs will be created at all. If an edge is selected,
then don't put a tab on this edge or its partner, overriding the default.
- Single-Tabs. A tab will be created on just one edge in each
edge-pair to be joined. If an edge is selected, then only use one tab between
this edge and its partner. Select this option a second time to flip which edge
has the tab.
- Double-Tabs. Tabs will be created on all edges around each nets.
If an edge is selected, then a tab will be put on both this edge and its
partner, regardless of the global default.
- Tab Size. Set how big you want your tabs. You can probably stick
with the default 0.5 cms.
Before printing out nets, you are going to want to decide how big to make your
model. This is what the items on the "Scale" menu are for. They let
you change the scale of the whole model by specifying the length of certain
features, such as edge length or radius. Note: the model does not get bigger
or smaller on the screen, but printed nets
will reflect the change in scale. However, if you have tabs on your nets, then
you will see them change size. Visually, they scale in the opposite direction
to the change you make, because while the model might be physically bigger, it
remains the same size on the screen, so the tabs which have remained the same
physical size, are therefore shown to be smaller.
Tip: You may enter an equation rather than a
simple number if you wish.
Here's what the items on the Scale menu do:
- Fit Nets to Pages
This adjusts the scale of the current model so that the largest net just fits
on a page. Use this if you want to make the model as big as possible, given
the nets you want to print out.
- Base Polyhedron Radius...
Tells you the radius of the base polyhedron, and lets you change it.
- Base Circumference...
Shows and allows you to edit the circumference of the base polyhedron's
circumsphere.
- Edge Length...
Tells you the length of the selected edge, and allows you to change it. If no
edge is selected, it tells you the shortest and longest edge length in the base
or dual polyhedron (depending on selected view), and allows you to change the
longest edge length.
- Base Polyhedron Inradius...
Tells you the inradius of the base polyhedron, if it has one. The inradius is
the radius of a sphere that just touches each face plane (that is, the face
planes are tangent to it). If there is not a single inradius, then it shows
you the distance of the selected face plane from the model's centre. You can
edit the value in either case to change the scale of the model.
- Base Polyhedron Surface Area...
Tells you the surface area of the base polyhedron, and lets you change it.
- Base Polyhedron Volume...
Tells you the volume of the base polyhedron, and lets you change it.
- Dual Radius...
Tells you the radius of the dual polyhedron, and lets you change it.
- Dual Inradius...
Tells you the inradius of the dual polyhedron, and lets you change it.
- Dual Surface Area...
Tells you the surface area of the dual polyhedron, and lets you change it.
- Dual Volume...
Tells you the volume of the dual polyhedron, and lets you change it.
- Midradius / Reciprocation Radius...
Tells you the midradius of the polyhedron, and lets you change it. This value
is really the radius of the sphere used for reciprocation (the process used to
create the dual). For uniform polyhedra (e.g. Platonic and Archimedean solids)
it will be the midradius, i.e. the distance from the model's centre to lines
through each of its edges. For other models it may be an approximation, as
such models may not have a single midradius.
- Shortest Edge Length...
Tells you the length of the shortest required in the nets, and lets you change
it. This is useful because edges become too fiddly when they're too small. I
always check this before making a model.
- Measured Distance...
Tells you the radius of the current measured distance when using
Measurement Mode, and lets you change it.
- Stretch (Non-Uniform Scale)...
This item is different from the others above. Rather than just setting the
size of the model for which nets are printed, this item actually changes the
model, by stretching or squashing it in some direction. You may choose to
scale it along one of its symmetry axes, or perpendicular to the selected face,
along a selected edge, or through a selected vertex. You may scale by a given
factor, or set the resulting height of the model explicitly. You can even set
the resulting length of the currently measured distance in
Measurement Mode, which allows you, for example, to
set the resulting length of lateral edges of an antiprism.
- Distance Units
Lets you choose what units to use for distances. Available units are:
millimetres, centimetres, metres, inches and feet.
- Angle Units
Lets you choose what units to use for angles. Available units are:
degrees (decimal), degrees/minutes/seconds and radians. This affects how
angles are displayed when using "Nets→Show Edge Data→Dihedral
Angles", for example.
Tip: When entering a scale, or entering a real
number in any other part of the interface, you may enter an equation rather
than a simple number if you wish. Examples of equations include:
- 1 / 5. A fifth, same as 0.2.
- 3.1 + 2.5 * 3. As usual, multiplication takes place before addition.
- (2 - 1) * (3 + 1). Brackets may be used to force operator
precedence the way you want.
- 2 ^ 7. 2 to the power of 7.
- 2 + 1 / tau. "tau" or "g" may be used to represent the golden ratio
(1.618034...). You may also use "pi" (3.14159...).
- sqrt(2). Square root of 2. Other functions available include sin(),
cos() and tan(), which expect radians as input, or their equivalents expecting
degrees: sind(), cosd() and tand().
- 1 + 3r2. "r" may be used as shorthand for sqrt(). Brackets are not
required if taking the square root of a simple number. Also, multiplication is
presumed when "*" is left out, so "3r2" may be used instead of "3 * r2".
Most operations can be undone and redone, including changing to a new model,
changing the scale of the model, and changing face colors and images. Use
"Edit→Undo" (keyboard shortcut: Ctrl+Z) to undo, and
"Edit→Redo" (keyboard shortcut: Ctrl+R) to redo. Both
operations are also available on the main toolbar. If you
Right-click on either button, you'll see a menu of the last 20
operations that can be undone/redone. Select one to perform multiple
undos/redos in a single step.
See also "Edit→Undo Settings" for various options that control
the undo mechanism. You may limit the amount of memory used, and the number of
undo levels available.
Expand any view temporarily to become full-screen using F2 or
"View→Full Screen". The active view then takes over the screen and all
menus, toolbars and borders are hidden. It can be nice to view models this way
with no other distractions. To exit this mode, hit F2 again, or hit
Esc. Any operation that opens a dialog box will
also force an exit from full screen mode (e.g. opening a file with
Ctrl+O).
Geometry may be viewed in true stereoscopic 3D! To enable this, select from
the "Display→3D Stereo Display" submenu. Two slightly different
images will be rendered, one for each eye, giving the model a 3D appearance.
If you load a background image ("Image→Load Background Image"),
it will appear to be pushed back behind the model.
If you have red/blue or red/green glasses, you may use those. Even with
red/blue glasses, try the "Left Red, Right Cyan" option as it may work
better than the "Left Red, Right Blue" option. If you're after some
red/blue glasses, there are some available for under $3 including shipping
here.
The other option is to display the two images for your left and right eye
side-by-side. You have the option of putting them either way around. This
option has the advantage of maintaining full-color images and not requiring
glasses, but requires the user to be able to blend the two images themselves,
either by going slightly cross-eyed, or by allowing their eyes to drift apart
slightly. For the cross-eyed option, try holding a finger to the screen,
pointing up, with the tip between the two images, then pull the finger slowly
towards yourself. Keep your eyes focused on your finger but be aware of the
two images behind it. There will be a point where they overlap behind your
finger. Now try to keep those images fused and slowly take your finger away.
Personally I find the parallel-eyed version much easier to achieve and to
keep focused. For this, try to look past the screen into the distance and
focus far away. Then try to look down to the screen while keeping your eyes
focused in the distance. Again it is a matter of then trying to merge the two
images.
When changing from one polyhedron to another, the transition may be animated,
and there are plenty of ways to customise this. You can control what kind of
transitions is used in different situations, as well as adjusting parameters
governing how each type of transition behaves.
Tip: You can skip a transition at any time by hitting
Esc.
The first two items on the Options menu relate to transitions:
- Enable Transitions: Use this to enable or disable transitions. You
may want to disable them in order to race through polyhedra more quickly.
However you might want to consider reducing the default transition time from
half a second to something even faster instead. More snappy, but still has a
nice feel to it.
- Transition Options: Opens the Transitions dialog box.
The Transitions dialog box has a great many options for customising
transitions, but you needn't understand them all. If you just want to change
the type of transition, or the length of each transition, then make sure
"Occasion" is set to "Default", and change "Method" or "Duration" accordingly.
See below for a list of methods available.
The Transitions dialog box is modeless, meaning you can leave it open and
still use the rest of the program. This lets you see what effect changing
settings has without closing the window.
If you want to get into more detail, here's what the Transition dialog box
provides:
- Setup: The complete set of transition options may be saved and
reloaded later. Choose an existing setup from the drop-down list, or enter the
name of a new setup. A number of predefined setups are built in. The
selection has no effect until you click one of the following buttons:
- Load: Load the selected setup, if it exists.
- Save: Save over the selected setup. Built-in predefined setups
can't be replaced.
- Delete: Delete the selected setup. Built-in predefined setups
can't be deleted.
- Occasion: Choose the occasion whose transitions you wish to edit.
This will populate the remaining settings to reflect the current settings for
that occasion. A line of text appears below here with a helpful note about the
selected occasion. Occasions to choose from are as follows:
- Default: These settings are used for any occasion that doesn't
specify its own non-default settings.
- Selected tour events: This lets you change the transitions for
one or more selected tour events.
See Tours below for information about tours.
- Start-up: This transition only occurs when first starting the
program.
- Load built-in model: Transition occurs when a
built-in model is loaded, e.g. when clicking the
right-pointing green arrow to move to the next model. If you hit the
left-pointing green arrow to move to the previous model, the inverse
transition is used. For example, if the transition normally moves the new
and old models to the left, then the inverse transition moves them to the
right. This gives a more intuitive feel as you move forward and backward
through the list.
- Load from file: Transition occurs when loading a model from a
file. Inverse transition is used when moving to previous file in a folder.
- <Multiple occasions...>: Allows you to set transition
options for multiple occasions at once. Opens a list of occasions where
you can tick any combination. Options that currently vary between
occasions will show <No change> until you set them
otherwise, and their drop-downs will show all the individual current values
for quick selection.
- Method: Select the method to use for transitions. All settings from
here on apply to the current occasion only, as set above. Each transition
method has a few settings to tweak its behaviour. The methods are as follows:
- No transition: Instant change.
- Random: Select a transition type at random.
- Sideways: The old model spins off one side while the new model
spins on from the other side. Settings are:
- Angle: Angle of movement. Zero represents movement from
right to left, 90 is top to bottom, 180 right to left etc.
- Fade-out spin: When non-zero, then model will spin faster
and faster as it moves off the screen, ending with the rate set here
just before it vanishes. The rate is given in full rotations per
second.
- Orbit: The old and new models orbit each other as one grows and
the other shrinks. Has the following settings:
- Tilt angle: Tilt angle of the orbit axis.
- Number of orbits: Number of complete orbits around each
other.
- Fade-out spin: Same as for the Sideways method above.
- Shrink & Grow: One model shrinks in-place while the other
grows. Just one setting:
- Fade-out spin: Same as for the Sideways method above.
- Explode & Grow: Old model explodes while the new model grows
from inside. See below for settings.
- Shrink & Implode: Old model shrinks while new model implodes
to enclose it. See below for settings.
- Explode & Implode: Old model explodes while new model
implodes into place. Settings for this and the above two options are as
follows:
- Explosion size: Relative size of fully exploded model. "1"
represents same as original.
- Fade-out spin: Same as for the Sideways method above.
A tour is an animated polyhedral slideshow. For example, you may start
with a cube folding and unfolding, then switch to a dodecahedron morphing into
its dual and back, and so on. You may choose the transition to use between
each event, and may even transition between 3D and 2D views.
Tip: You can stop a tour from playing back by hitting
Esc (or by hitting the play button again).
A tour consists of a list of events. Each event may have its own model,
view layout, and transition to the next event.
Tours can be saved and reloaded from .tour files.
The Tour menu provides various controls for creating and editing
your tour. The Tour toolbar provides another way to access all these same
controls. The menu contains the following:
- Show/Hide Tour List: Show or hide the tour list, which lists all
events in the current tour. More on this below.
- Open Tour: Browse to open a tour file.
- Merge Tour: Find a tour file to merge into the current tour.
Events from the tour file are appended to the end of the current list.
- Save Tour: Browse to save the current tour.
- Play Tour: Play the tour. While playing a small play-symbol appears
next to the mouse pointer. Use this control again to stop playing the tour, or
hit Esc. The tour also stops playing if you click
on another item in the tour.
- Add to Tour: Add the currently loaded model and view layout to the
tour list. It is added at the end, but you may then drag it in the list to any
position you want.
- Replace Current Event: Replace the current event with the current
model. For example, you might select an event, make changes to how fast it's
spinning or folding, then save these changes back over the original event.
- Remove from Tour: Remove the currently selected event or events from
the tour.
- Previous Event: Step to the previous event in the tour.
- Next Event: Step to the next event in the tour.
The tour list shows all the events in a list, one per row. You may drag
items within the list to rearrange them. You may click on an event to select
it, and use Ctrl+Left-click to select multiple events. The list has
columns, each showing different information about each event, including:
- Name: Name of the tour event. After selecting, click in this field
again to edit the name.
- Duration: Duration of event in seconds, not including transition
time between events. Click again once selected to edit.
- Fade: Duration of transition between this event and the next. If it
shows <Default>, then the default transition duration is used.
Click again once selected to edit. Enter a time in seconds, or -1 to use the
default.
- Fade Type: The transition method to be used between this event and
the next. Click again once selected to choose another method.
- Inherit Layout: When "No", the view layout and rate of spinning,
folding, morphing etc are all loaded from this event. When "Yes", all this
information is inherited. Use "Yes" when you want to go from one event to
another but keep the same rate of rotation and same orientation etc.
Click to switch between "Yes" and "No".
You may Right-click on the tour list to open a menu with a few
relevant options:
- Set Duration: Set the duration of the selected events.
This is more powerful than editing the duration in-place in the list, because
you may select multiple events first.
- Transition Options: Open the Transition dialog box (see
above) and set the occasion to "Selected tour
events", allowing you to edit all the transition options for one or more tour
events.
- Inherit Layout: Switch the inherit-layout flag on or off for all
selected events.
- Delete: Delete the selected events.
Overall display of vertices and edges may be enabled or disabled. They may
be shown either as points and lines, or spheres and cylinders respectively.
All settings are remembered after you exit the program for next time.
Tip: To hide or show individual vertices or edges, see
Hiding Individual Faces, Edges and Vertices
below.
Options for controlling the overall display of vertices and edges are found on
the "Display→Vertex & Edge Options" submenu:
- Show Vertices (keyboard shortcut: V).
Enable this option to display a small point or sphere at each vertex of the
model.
Note: only true vertices are shown, not virtual ones where faces
intersect.
- Show Edges (keyboard shortcut: E).
Enable this option to display a line or cylinder along each edge of the
model.
Note: only true edges are shown, not virtual ones where faces
intersect.
- Size for Drawing Vertices. Allows you to adjust the size of the
points displayed at each vertex.
Tip: Right-click on the Show Vertices toolbar button to
open a small menu where you can quickly choose this option.
- Line Width for Edges. Allows you to adjust the width of lines
displayed along each edge.
Tip: Right-click on the Show Edges toolbar button to
open a small menu where you can quickly choose this option.
- Use Spheres and Cylinders. Select this option to display
spheres and cylinders rather than points and lines at vertices and
edges respectively.
- Sphere and Cylinder Options. Opens
a window allowing control of various options for displaying spheres and
cylinders. The window is modeless, so you can still use the rest of
the program while this window is open, and immediately see the effects of
your changes. You may specify the material used (solid color, same as
points/lines, gold, silver, copper, wood or stone). You may also set the
radius of the spheres and cylinders. The cylinder radius is set as a
fraction of the sphere radius (e.g. 0.5 for half the radius). The sphere
radius is generally also set as a fraction of another value. That value
may be chosen from the following choices:
- Inverse square root of number of edges. This may sound like
a somewhat arbitrary choice, but I found it through much
experimentation and it works very well for a wide range of models.
Generally, the more edges there are, the smaller you want the spheres,
which is what this achieves. For this reason it is the default
setting.
- Edge length of model. You may want the cylinder radius to
be proportional to the edge length.
- Radius of model. Here the sphere radius is proportional to
the physical size of the model, but not the complexity.
- Specify actual measurement. Rather than a fraction of some
other measurement, this allows you to explicitly enter the sphere
radius.
Tip: Right-click on the Use Spheres and Cylinders toolbar
button to quickly open this options window.
The Display menu includes a group of items for hiding or showing
individual faces, edges or vertices. Most of these require you to
select a face, edge or vertex first (see
Selecting Faces, Edges and Vertices).
Tip: Make sure you have overall display of vertices
and/or edges enabled, or they will always be hidden.
Tip: Vertices and their dual faces are hidden in sync. So when you hide
an individual vertex, it will hide the matching dual face too.
When a vertex or edge is selected, the text in the menu items
below will have "Face" replaced by
"Vertex" or "Edge" as appropriate.
The relevant items from the Display menu are as follows.
- Show/Hide Faces of Selected Color (keyboard shortcut: H).
The selected face/edge/vertex is hidden along with all others
of the same color. If any were already hidden, then all are unhidden instead.
- Show/Hide Faces of Selected Type (keyboard shortcut: Shift+H).
The selected face/edge/vertex is hidden along with all others
of the same type. If any were already hidden, then all are unhidden instead.
- Show/Hide Selected Face (keyboard shortcut: Ctrl+H).
The selected face/edge/vertex is hidden. If it was already
hidden, then it is unhidden instead.
- Show/Hide All Faces (keyboard shortcut: Ctrl+Shift+H).
All faces/edges/vertices are hidden. If any were already
hidden, then all are unhidden instead.
- Toggle Shown/Hidden Faces (keyboard shortcut: Ctrl+Shift+T).
All hidden faces/edges/vertices become unhidden, and all those
unhidden become hidden. This is useful when you want only a few faces
displayed: start by hiding the faces of interest, then toggle so that all other
faces are hidden instead. Similarly, unhiding a specific face can be tricky
since you can't select it with the mouse. Start by toggling all hidden faces,
then select the face of interest and hide it, then toggle again.
- Show/Hide Faces in Selected Plane. Hide all faces in the same plane
as the selected face. If they are all hidden already, then they are all
unhidden. This option applies to faces only.
- Show/Hide One Part of Compound. Hide one whole part of a compound
(the one with the selected face). If already hidden, it is
unhidden instead.
- Show/Hide Faces Around Vertex (keyboard shortcut: Ctrl+Shift+V).
All faces around a specific vertex are hidden. If any were already hidden,
then they are all unhidden instead. A window appears allowing you to enter the
index of the vertex to use. If you select a vertex first with the mouse, then
the index will default to that vertex, so you can just click OK or hit
Enter.
- Hide Edges & Vertices Between Hidden Faces. This item is a
setting which may be enabled or disabled, rather than a one-off action. When
enabled, any edges or vertices surrounded only by hidden faces will also be
hidden, regardless of whether they have otherwise been flagged as hidden.
Note, the hidden attribute of a face can also be copied
quickly between faces using
Color/Hide Faces Mode.
Models may be colored in various ways. This section describes the items on
the Color menu. See also
Color/Hide Faces Mode for rapidly spreading colors
across selected faces.
- Rainbow Color Mode (keyboard shortcut: Shift+R).
This turns Rainbow mode on and off. Rainbow mode overrides all
other color settings. It draws models in white only, but uses three
lights in the colors red, green and blue. This makes the faces change to
all sorts of colors as a model is rotated, and makes it easy to
distinguish between faces. It is similar to the coloring style used by
the program Mathematica.
- Basic Color Scheme. This submenu lets you choose the basic
color scheme that will be used to color the faces. There are three
groups of options here:
- Exactly one option at a time may be selected from the first group.
With the exception of "Auto Color", they are listed roughly
from the least to the most colorful.
- Auto Color. This is the default setting.
Firstly, if the model is a compound, then each component is given
its own color. Otherwise, the polyhedron is colored according to
face type. If there's only one face type, a different color is
used for the front and back of faces, to make it more colorful. If
there are greater than 5 face types, chiral pairs are colored the
same way to reduce the number of colors and highlight reflective
symmetry.
- Use a Single Color. A single color is used for all
faces of the model.
- Color Faces by Number of Sides. All triangles will use
one color, all quadrilaterals another color, all pentagons another
color and so on. For example, there are two different types
of triangle in the snub cube, but they are both given the same
color using this method.
- Color by Face Type. Each type of face is given its own
color. Faces are of the same type if they fit into the
model the same way. The snub cube, for example, has two different
types of triangle faces. One has another triangle across each
edge, and one has a square across one of its edges. So these would
be colored differently using this method. The next group of
options below can be used to tweak this behaviour.
- Color Along Cross-Section Direction. Faces within each
type are colored differently depending on how far along the
cross-section direction they occur (this is an axis orthogonal to
the cross-section plane). The main purpose of this is to make
cross-sections more colorful, while still retaining their own color
symmetry. See Cross-Sections.
- Color per Face (Unless Parallel). Every face is given
its own color, unless they are parallel. All parallel faces are
given the same color with this method (even if they are not the
same shape).
- The second group of options may be enabled independently. They are
all available when using "Color by Face Type" from the first
group of options above. Otherwise some options will not be available,
as appropriate.
- Same Color for Chiral Face Pairs. Faces that are
mirror images of each other will be colored the same.
- Same Color for Coplanar Faces. Coplanar faces will
always be colored the same.
- Same Color for Coplanar Chiral Pairs. Faces that are
coplanar and mirror images of each other will be colored the same.
- Same Color for Front and Back of Faces. The front and
back of each face will be colored the same.
- The final group contains just one item:
- Toggle Single/Auto Color Modes (keyboard shortcut:
Tab). To switch between single and auto coloring modes.
- Special Color Arrangements. This submenu lets you choose a
predefined color arrangement, for faces with certain symmetry. You may
choose one arrangement for each kind of symmetry, or select it again to
disable it. Any settings here will override the basic color scheme set
above (for the relevant faces only). The first dodecahedral and first two
icosahedral arrangements are as described in Magnus Wenninger's
Polyhedron Models.
- Dodecahedral Arrangement 1 (4 colors).
- Dodecahedral Arrangement 2 (6 colors).
- Icosahedral Arrangement 1 (5 colors).
- Icosahedral Arrangement 2 (5 colors).
- Icosahedral Arrangement 3 (10 colors).
- Rhombic Triacontahedral Arr 1 (5 colors).
- Rhombic Triacontahedral Arr 2 (15 colors).
- Cubic Arrangement (3 colors).
- Octahedral Arrangement (4 colors).
- Rhombic Dodecahedral Arr 1 (3 colors).
- Rhombic Dodecahedral Arr 2 (4 colors).
- Rhombic Dodecahedral Arr 3 (6 colors).
For example, to color the truncated dodecahedron, and avoid any faces of
the same color sharing an edge, you might set the basic color scheme to
"Auto Color" and enable the first dodecahedral arrangement. Since
we haven't chosen a special icosahedral arrangement, the icosahedral
triangles would all be the same color, which is fine because they don't
share edges with each other. The dodecahedral arrangement however, will
use four different colors for the decagrams, ensuring that decagrams of the
same color will never share an edge.
- Replace Face Color Throughout... (keyboard shortcut: C).
Change the color of all faces with the same color as the selected face, in
both the base model and the dual. Backs of faces which are the same color
are also changed. The user is prompted for a new color.
If an edge or vertex has been selected, then the operation applies to edges
or vertices instead. Note: individual coloring of vertices is only
possible when "Color→Color Vertices Same as Dual Face" is
enabled.
- Set Face-Type Color... (keyboard shortcut: Shift+C).
Change the color (front and back) of all faces of the same type as the
selected face.
If an edge or vertex has been selected, then the operation applies to edges
or vertices instead. Note: individual coloring of vertices is only
possible when "Color→Color Vertices Same as Dual Face" is
enabled.
- Set Single Face Color... (keyboard shortcut: Ctrl+C).
Change the color of the selected face only. If the back of the face is the
same color as the front, then it is also changed.
If an edge or vertex has been selected, then the operation applies to that
edge or vertex instead. Note: individual coloring of vertices is only
possible when "Color→Color Vertices Same as Dual Face" is
enabled.
- Set all Face Colors... (keyboard shortcut: Ctrl+Shift+C).
Change the color of all the faces, front and back.
If an edge or vertex has been selected, then the operation applies to edges
or vertices instead. Note: individual coloring of vertices is only
possible when "Color→Color Vertices Same as Dual Face" is
enabled.
- Replace Back-Face Color Throughout... (keyboard shortcut:
B). Change the color of all backs of faces with the same color as the
back of the selected face.
- Set Back-Face-Type Color... (keyboard shortcut: Shift+B).
Change the color of the backs of all faces of the same type as the selected
face.
- Set Single Back-Face Color... (keyboard shortcut:
Ctrl+B). Change the color of the back of the selected face only.
- Set all Back-Face Colors... (keyboard shortcut:
Ctrl+Shift+B). Change the color of the backs of all the faces.
- Vertex Colors. Submenu for control over vertex colors.
Tip: Right-click on the Show Vertices toolbar button to open a
small menu where you can quickly choose these options.
- Default Vertex Color.... Change the default color used to
display vertices when shown as points, or when displayed as spheres if
sphere color has been set to match point color. To control the color used
when shown as spheres, use "Display→Vertex
& Edge Options→Sphere and Cylinder Options".
- Color Vertices Same as Dual Face. When ticked, vertices may be
colored individually, their colors being kept in sync with their dual
faces. Thus changing a vertex color will also change the matching dual
face color. In this case, the default vertex color is ignored.
- Edge Colors. Submenu for control over edge colors.
Tip: Right-click on the Show Edges toolbar button to open a
small menu where you can quickly choose these options.
- Default Edge Color.... Change the default color used to display
edges when shown as lines, or when displayed as cylinders if cylinder color
has been set to match line color. To change the color used when shown as
cylinders, use "Display→Vertex & Edge
Options→Sphere and Cylinder Options".
- Color All Edges the Same. The remaining options on this submenu
represent different coloring schemes for edges. Exactly one will be active
at any given time. This first option simply colors all edges the same,
using the default edge color.
- Color Edges by Type (including reflections). Each edge type is
given its own color. Edge types which are mirror reflections of each other
are also colored the same.
- Color Edges by Type (excluding reflections). Each edge type is
given its own color, but edge types which are mirror reflections of each
other are colored differently.
- Color Edges Same if Parallel. Edges are colored the same only if
they are parallel.
- Color Edges by Great Circles. Edges are colored the same only if
the lie in the same planes through the centre of the model.
- Color Edges from Neighbouring Faces. Edge colors are set by
averaging the colors of connected faces.
- Color Edges from Neighbouring Faces (complement). Edge colors
are set by averaging the colors of connected faces, and taking its
complement, making them stand out better against those faces.
- Set Midsphere Color.... Change the color used to display the
wire-frame sphere when "Display→Show Midsphere/Reciprocation
Sphere" is enabled.
- Set Background Color... (keyboard shortcut: G). Change
the background color. The user is prompted for a new color.
Images may be put on faces. You may want photos of your pets on the faces
of a dodecahedron, or you may want a model to look like it's made of wood.
This section describes the items on the Image menu (see also
Image mode below).
- Load Image... (keyboard shortcut: Ctrl+I).
Load an image from a file to display on the selected face. A file browser
appears allowing you to find the image you want. Select an image in the
browser to see a preview of the image along with its dimensions. Once an
image is opened, a window with various image options. This window is
similar to the one available with Image Options below.
- Load Image List.... Load a text file which contains a list of
image files to load. Select a text file in the browser to see a preview of
the first couple of lines. The file contains one file name per line. File
names are relative to the text file, or full paths can be given. Blank
lines are ignored, and comments may be included in the file after "#".
Each image is applied to a single face. Hidden faces are skipped. A
window with image options appears, allowing the user to set options which
will apply to all images loaded. It also gives a choice about which faces
the images should be applied to.
- Save Image List.... Save a text file containing the list of
images on faces of the current model.
- Persistent Image List. When enabled, a loaded list of images
will be remembered and re-loaded onto any new model that's loaded.
- Apply Image to Other Faces.... Apply the image on the selected
face to other additional faces. Gives the user the following options:
- All faces of same type as selected face
- All faces with same color as selected face
- All faces with no image
- All faces
- Cancel
Another way to apply an existing image to new faces is to use Color Mode (see below).
- Remove Images.... Remove images from some or all faces.
A list of options is presented to the user, similar to above.
- Image Options.... Opens a window with various image options.
The options are also available directly elsewhere on this menu, so see
above and below for details of what the options do. This window provides a
convenient way to set multiple options at one time, and there is a preview
in the bottom right corner which shows you the effect of an option as you
move the mouse over it.
Tip: Right-click on the Image mode toolbar button to open a
small menu where you can quickly choose this option.
- Options for All Images.... Opens a window similar to above, but
options set here will be applied to all images on the current model. Only
set the options you wish to change.
Tip: Right-click on the Image mode toolbar button to open a
small menu where you can quickly choose this option.
- Image Projection. Submenu with various projection types for
mapping images onto a model.
- Project onto each Face Separately. Image is projected onto
each face individually, as if a separate copy is lying flat on each
face.
- Planar. Single image is projected through the whole model.
Works well for a wood-grain or marble image. It will appear stretched
on faces that are at a sharp angle to the image.
- Cylindrical. Image is wrapped around model in a cylindrical
fashion. Less stretching at the sides, but there still may be
stretching for faces at the top and bottom.
- Spherical. Image is wrapped onto a sphere and projected
inwards through the model. This has the least stretching, although the
wrapping onto a sphere itself may stretch the image near the top and
bottom if the image was not designed for spherical mapping.
- Image Orientation. Submenu specifying what orientation to map
the image.
- Project Towards Selected Item. Image is projected towards a
selected face, edge, vertex or rotational symmetry axis.
- Align Height of Image to Selected Item. Use this one to
align the axis for cylindrical or spherical mapping to a selected face,
edge, vertex or rotational symmetry axis.
- Fit Image Within Face. Resize and reposition the image so that
it fits entirely within the selected face.
- Fit Image Around.... A submenu which lets you resize and
reposition the image so that it fits tightly around the selected face, over
the entire model, or over all those faces with the image applied.
- Unstretch Image. An image can be stretched in Image
mode (see below). Use this option to
unstretch it again.
- Flip Image Horizontally. Use this if your image is
back-to-front.
- Keep Image Upright. Keeps images upright on faces regardless of
the orientation of the model. Only works when "Project onto each Face
Separately" is chosen from the "Image Mapping" submenu (see
above).
- When Rotating, Snap Image to Edges. When rotating an image in
Image mode (see below), snap to
orientations where an edge of the image is parallel to an edge of the
selected face. If "Keep Image Upright" is enabled (see above),
then rotation snaps when image is close to landscape or portrait instead.
When this option is disabled, you may freely rotate to any angle.
- Show Whole Image in Image Mode. When in Image mode
(see below), show a transparent version of the
entire image, even though it may extend off the edge of the model. This
makes it easier to see what part of the image is on a face, and how close
to the edges you are etc. Disable if this is distracting. When a face is
selected, feint lines are also drawn on the image to indicate the face
mapping.
- Blocky Pixels when Close-Up. When ticked, you may zoom in to
see an image's sharp-edged pixels. Otherwise, the pixels will be smoothed
(the default).
- Image Boundaries. A submenu which lets you choose what happens
outside the edges of the image. An endless border of any color may be used
around the image, or the image may be repeated endlessly, or values can
be clamped to the edges of the image.
- Use Face Color in Addition to Image. Normally when you put an
image on a face, you don't also want the original color of the face to show
through, but enable this option if you do want it to show through. You may
create some interesting effects by mixing a color with your image.
- Load Background Image. Opens a file browser, allowing the user
to find an image which should be displayed in the background. Select an
image in the browser to see a preview of the image in the browser.
- Remove Background Image. Stop showing an image in the
background.
- Background Image Fit. Submenu for choosing how background image
should fit within each view.
- Fit Within. Background image is scaled to just fit within
each view. Space left at the top or sides is filled with the usual
background color.
- Fit Around. Background image is scaled to just fit around
each view, leaving no space uncovered. This may crop the image at the
sides or top.
- Fit Width. Background image is scaled so that its width
matches the width of each view. The top and bottom may be cropped,
or space may be left which is filled with the usual background color.
- Fit Height. Background image is scaled so that its height
matches the height of each view. The sides may be cropped, or space
may be left which is filled with the usual background color.
- Stretch. Background image is stretched to fit the width and
height in each view. This is the only option where the image's aspect
ratio is not maintained.
- Actual Image Size. Background image is shown at actual size
(pixels of the image mapping to pixels on the screen). The image may
be cropped, or space may be left around it, filled with the usual
background color.
- Show BG Image Through Model. Allows the background image to
show partially through the model, which may be handy if you're aligning
something. The value must be between 0.0, where the image won't show
through the model at all, and 0.95, where the image almost completely hides
the model. A value of 1.0 would hide the model completely which could lead
to confusion, so the 0.95 limit has been set.
- Maximum Image Size. Images can take up a lot of memory,
generally a lot more than the original size of the image file on your hard
drive (because it is no longer compressed). This option lets you limit the
size used internally for images. Digital cameras often create very large
images, but you won't see any difference on screen if smaller images are
used. You only need to tweak this value in two cases:
- Make it smaller if you are running out of graphics memory due to
lots of large images.
- Make it bigger if you don't think the resolution is high enough on
printed nets and pictures (printers are much higher resolution than
screens).
Rendering in Geomag style makes polyhedra appear as if they were built using
the Geomag magnetic construction
kit. Generally Geomag-style rendering will be permitted unless a model
could not be physically built using Geomag, in which case a reason will be
shown on the screen. Some common polygons not available from Geomag are
subdivided using ones that are.
Control Geomag-style rendering via the "Display→Geomag" submenu
(or matching toolbar buttons):
- Geomag Style. Enable or disable Geomag-style rendering.
- Subdivide Inwards. Geomag do not make octagons and decagons, so
cupolae are used in their place, constructed from squares and triangles.
However these are not flat, so this option decides whether such cupolae should
poke out or poke in.
- Geomag Edge Style. Submenu allowing you to select an edge style from
those available in the Geomag construction kit.
When selecting face colors, you will be limited to those available for Geomag
panels.
If images are applied to the faces, these will appear
as if using Geomag's Deko panels. When printing the unfolded net view, only
the parts you require for use with the Deko panels will be printed, ready to
cut out and insert into the Deko panels.
A collection of models suitable for construction with Geomag can be found in
the Geomag Library folder within the Stella
library.
Select a view and use "View→View Diagrams→Cross-Section" or
the matching toolbar button to switch to the Cross-Section view. This shows
a 2D cross-section (or slice) through the current polyhedron.
The cross-section is made with a slicing plane, which can be controlled
in various ways. Any edge of the original model passing through the plane is
sliced to become a vertex. Any face crossing the plane is sliced to become one
or more edges (nonconvex polygons can lead to more than one edge). And a whole
polyhedron is sliced to create one or more polygons. So each entity loses one
dimension as a result of the slicing process.
Note: many edges and faces may lie entirely on one side of the slicing plane,
and so do not contribute at all to the cross-section.
Cross-sections have a beauty all of their own, especially when animated by
altering the slicing depth (keeping the slicing plane parallel, but
moving it through the model). The slicing depth is a value between 0.0 and
1.0, each representing a plane at opposite ends of the model.
Each polygon of the 2D cross-section is surrounded by edges formed by
slicing faces. The edges are shown in the color of their corresponding face,
and the polygon itself is filled with a color obtained by averaging the colors
of its surrounding edges, weighted by their edge-lengths. This can produce
some pleasing results, with the polygon colors changing smoothly into other
colors as their edges get longer or shorter. When multiple polygons overlap,
the overlapping colors are also blended, making even more interesting images.
More colorful cross-sections can be obtained by using "Color→Basic
Color Scheme→Color Along Cross-Section Direction", especially for
regular polyhedra, which would normally be shown all in one color. When all
faces have the same color, the detail of the cross-section can be lost since
all edges and filled regions become the same color. With this option,
cross-sections become much more colorful, but still retain full color symmetry.
The mouse may be used in the following ways.
- Shift+Left-click: click on an edge to select the face it
represents.
- Shift+Right-click: same as Shift+Left-click.
- Ctrl+Left-drag: change the slicing depth. Mouse inertia
is supported as usual, so let go of the Left button while still dragging the
mouse and the animation should continue on its own at the current speed.
- Ctrl+Right-click: set the slicing depth to exactly
half-way. This is often a point of particular interest.
The Section menu offers further cross-sectioning options:
- Cross-Section Direction submenu:
Tip: Right-click on the Cross-Section Tumble Mode or the
View Cross-Section toolbar buttons to open a menu with these same
choices.
- Selected Face/Edge/Vertex/Symmetry First. Use the selected
face/edge/vertex/symmetry axis to decide the slicing direction. For a
face, the slicing plane will be parallel to the face. For a vertex, the
slicing plane will be orthogonal to a line through the vertex and the
centre of the polyhedron.
- Along N-fold Axis. Slice perpendicular to the
N-fold symmetry axis. N changes depending on the symmetry
group of the model. Three such menu items appear, for the (up to) three
different types of rotational symmetry present.
- Measured Item First. Slicing plane is defined by current item
defined in Measurement Mode (a point, line, or face). The slicing depth is
also set to align with the defined item (see
Measurement Mode).
- Automatic. When ticked, choose whatever seems like the nicest
cross-section direction whenever a new model is loaded. This is generally
whichever direction will lead to a cross-section with the most symmetry.
- Set Cross-Section Depth... Explicitly set the slicing depth to a
value between 0.0 and 1.0. As with all real number fields, you may also enter
an equation here.
- Snap Sectioning Depth to Vertex. Change the slicing depth (up or
down) so that the slicing plane passes through the nearest vertex from the
original model.
- Show Cross-Section in Model Views submenu:
- Always. Always show the cross-section embedded in the model
views (i.e. Base, Dual, and Base + Dual views). It can be helpful to see
how the cross-section fits into the original model. When embedded in this
way, using Ctrl+Left-drag and Ctrl+Right-click in the
model views behaves as it would in the Cross-Section view instead, that is,
to change the slicing depth.
- When Cross-Section View is Open. Only show the cross-section
embedded in the model views when there is a Cross-Section view open
elsewhere.
- Never. This is the default. Don't ever show the cross-section
in the model views.
- Show Vertices Near Slice Plane. When ticked, vertices of the
original model are displayed in the Cross-Section view when they get close to
the slicing plane. They are represented as white circles
which grow in size as the slicing plane approaches, then shrink again as it
passes by. They become green if they lie precisely in the slicing plane. It
is as if spheres were placed at each original vertex, and they too were being
cross-sectioned to create circles.
- Fill 2D Cross-Section. Untick this option to show cross-sections
only as an unfilled outline. For extremely complex models, the filling can be
very slow, so untick this option if you find such a model. Outline-only
cross-sections can be displayed almost instantly for any model.
- Show 2D Cross-Section Edges. Untick this option to show
cross-sections as filled areas only with no outline. Sometimes this is
aesthetically more pleasing, giving a "smoother" appearance.
The yellow left/right buttons in the title bar of the Cross-Section view
also serve a purpose. They skip the slicing depth forward or backward to all
the values where the slicing plane passes through a vertex of the original
model. These are often quite interesting points in the transition.
Finally, the slicing plane can be tumbled interactively in a free-form
style. See Cross-Section Tumble Mode for the details.
Symmetries are transformations which leave a model looking like it
hasn't moved. They mostly come in two types: rotational and reflective. Use
"Display→Show Symmetry Axes" to display the rotational symmetry
axes (keyboard shortcut: S, also on options toolbar). In 3D views these
are indicated by an axis through the model with a small disc at either end.
The number of spokes in the disc indicates the order of rotational symmetry.
The different types of rotational symmetry axis are shown in different colors.
Use "Display→Show Reflection Planes" to display the reflective
symmetries (keyboard shortcut: R, also on options toolbar). In 3D views these are
represented by great circles around the model in the reflection plane.
The symmetry group of a polyhedron is the collection of all its
symmetries. The options toolbar has a field that shows the rotational
symmetry group (e.g. "Icosahedral"), and another field showing the reflective
symmetry group within that (e.g. "Horizontal Reflection"). To the left of
these is another field showing two common symbols used for the current symmetry
group: Schönflies notation, Orbifold notation, and Coxeter notation.
Read about symmetry groups and their notations at
https://en.wikipedia.org/wiki/List_of_spherical_symmetry_groups.
Another good web page showing the different symmetry groups
is
http://newton.ex.ac.uk/research/qsystems/people/goss/symmetry/Solids.html.
The only groups missing from this site are icosahedral symmetry, both with and
without reflections. The h subscripts on that page correspond to
"Horizontal Reflection" in Stella, and the d subscripts
correspond to "Diagonal Reflection". Notice that the rotational symmetries of
a tetrahedron can be combined with either of these reflection types
(Th and Td). The latter is the symmetry
group of the regular tetrahedron, while the former is known as
pyritohedral symmetry.
Submenu: "Selection→Mouse Selection Mode"
Items in this submenu allow you to enter a different mode, where the mouse
behaves differently from normal. Exactly one of the items will be selected at
any one time. The first item on the list is the default mode, so to exit one
of the other modes, either select this item, or just hit
Esc. There is also a toolbar containing a button
for each of these modes.
You can tell when you're in a different mode from usual by holding down
Shift and seeing what shape the mouse pointer becomes. Navigation
with the mouse acts the same in all modes. The difference is what happens when
you're holding down Shift and/or Ctrl.
Some of these modes are described in the following sections.
Menu item: "Selection→Mouse Selection Mode→Cut/Uncut Edges"
If you don't like the net created, you can force the program to cut
certain edges. This makes it rebuild the nets, connecting different
faces together instead.
- Shift+Left-click: Cut/uncut edges of selected type.
- Shift+Right-click: Cut/uncut a single edge.
Uncutting an edge does not guarantee the faces will be attached in the net,
just stops them from being forcibly cut.
Note that cutting one edge may cause other faces to join together in a net
where they were previously not connected. This is because the nets are rebuilt
from scratch. So you can use cutting as a way of forcing other faces to join
up, but only indirectly. If you didn't want those faces to connect, then you
can always cut their shared edge too.
As an example, use Shift+Left-click on an edge of the icosahedron.
All edges are the same type, so they are all cut, so you end up with only one
face in each net. Use Shift+Right-click instead to cut just one edge.
Menu item: "Selection→Mouse Selection Mode→Measurement Mode"
Measurement Mode lets you measure the distance and angle between any two items,
where each item may be a
plane, line or point. The distance and angle are shown on the screen, and the
items highlighted in light blue, along with some construction lines to help
clarify what's being measured. Items may be defined via the mouse:
- Shift+Left-click: Select a new item.
- Shift+Right-click: Extend current item.
- Ctrl+Left-click: Replace most recent item with selected
one.
- Ctrl+Right-click: Extend current item.
So use Shift+Left-click to select a vertex, edge or face, and then
again to select another and see the distance and angle between them. If you
want to specify an item that doesn't correspond to an existing entity, such as
a plane through three arbitrary vertices, then you can build up this plane by
specifying each vertex in turn. Use Shift+Left-click for the first
one, then use Shift+Right-click to add the others. You can even
specify a plane through an edge and a vertex by
Shift+Left-clicking the first and
Shift+Right-clicking the second.
Normally at most two items are remembered at a time, and the distance and
angle measured between them. So when you specify a new item, the oldest item
of the previous two is discarded. You can use Ctrl instead of
Shift with the above mouse operations if you want to replace the most
recent item rather than the oldest. This retains the earlier item, so is handy
if you want to fan out measurements from the same point repeatedly.
These is one occasion where three items are remembered rather than two.
This is when you select three vertices in a row. The distance between the last
two is shown, along with the angle subtended at the middle point.
You may also specific a point at the centre of the model, even when there's
no vertex there to click on. There's a button which appears on each view's
title bar when in Measurement Mode to achieve this. It shows a circle with a
dot in the middle. This allows you to measure distances from the centre of the
model. Or you can use it as the first point in a line or plane through other
arbitrary vertices or edges by using Shift+Right-click as above.
In addition to appearing on-screen, the distance and angle are shown in the
status bar at the bottom of the window. You can also access the currently
measured distance via "Scale→Measured Distance". This also
lets you change the distance, which affects the scale of
the whole model, as used for printing nets and some other operations.
Note, you may only click on true vertices of the model, not virtual
ones caused by intersecting faces.
Aside from measuring things, Measurement Mode has other uses.
The most recently defined item may be used in the following ways:
- To define the cross-section direction and depth. Use
"Section→Cross-Section Direction→Measured Item First". See
Cross-Sections.
Menu item: "Selection→Mouse Selection Mode→Color/Hide Faces"
This mode lets you easily copy colors, images, or "hiddenness" between
faces.
- Ctrl+Left-click: copy attributes from the previously
selected face to the clicked face.
- Shift+Left-click: copy attributes from the previously
selected face to all faces of the same type as the clicked face (use
"Options→Maintain Reflexibility" to choose whether reflected faces
should also be changed).
In either case, you may hold the left mouse button down and drag the mouse
across multiple faces to apply the color/image to all of them, like painting.
No need to click on each one.
If the selected face was hidden, then the "hiddenness" is copied, that is,
other faces may be easily hidden too by Ctrl+Left-clicking on
them. In this case the color/image of the face is not changed (it is presumed
that it is only the hiddenness that you are interested in copying).
- Ctrl+Right-click and Shift+Right-click:
select a face without changing its color. This lets you choose a new face to
start copying attributes from. In this mode, the face is only highlighted
white briefly when you select it, and then returns to its normal color, since
it is important to see true face colors in this mode.
If you plan to do a lot of augmentation (see
below), this mode can be useful. One of
the options when augmenting is to only augment faces of the same color. So
select one of the faces you want to augment, then copy that color to all the
other faces you want to augment. This lets you quickly and easily select a
collection of faces for augmentation.
Face colors may also be changed in various ways via the
Colors menu.
Menu item: "Selection→Mouse Selection Mode→Image Mode"
If the selected face does not already have an image on it when entering this
mode, a file browser will open allowing you to select one. This is the same as
if you had used "Image→Load Image" (see
Images above). You may cancel the file browser if you
wish to use Image mode without loading any new images.
Image mode lets you accurately position images on faces however you want.
- Shift+Left-drag: move an image on a face
- Shift+Right-drag: scale an image on a face
- Shift+Left+Right-drag: rotate an image on a face
- Ctrl+Left-click: select face without affecting image
- Ctrl+Right-drag: stretch image
- Ctrl+Shift+Left-click: swap image with previously selected
face
Compare these three operations with navigation in a 2D view. Notice the
similarity when you don't hold down Shift? This makes it easier to
remember which combination of buttons does what.
Use Ctrl+Left-click to select a face without affecting the
image on it. And use Ctrl+Right-drag to stretch an image on
a face (changes the aspect ratio of the image). Note: when using
spherical or cylindrical mapping, the image must always wrap all the way
around, so scaling and stretching the image both have the same effect, to scale
it vertically, but leave it wrapped all the way around horizontally.
Use Ctrl+Shift+Left-click to swap images between
two faces. The images are swapped between the face you click on, and the face
that was previously selected. This is useful in conjunction with
"Image→Load Image List...". You can load a bunch of images at
once, then swap them between faces to get the arrangement you want.
Menu item: "Selection→Mouse Selection Mode→Cross-section
Tumble Mode"
This mode allows you to interactively tumble the slicing plane. See
Cross-Sections for more information and ways to choose
specific orientations of interest for the plane.
In this mode, the mouse can be used in the following ways.
- Shift+Left-drag: rotate slicing plane
- Ctrl+Left-drag: change slicing depth
- Ctrl+Right-click: slice half-way (set slicing depth to
0.5).
Small Stella was written by Robert Webb.
I use FreeImage
(http://freeimage.sourceforge.net,
under the FreeImage Public License version
1.0) for importing
2D images, which in turn uses various other
libraries. Below is a list of credits regarding these libraries:
- IJG JPEG library © 1994-1998, Thomas G. Lane
- LibPNG © 1998-2001 Glenn Randers-Pehrson
- LibTIFF © 1988-1997 Sam Leffler, © 1991-1997 Silicon Graphics Inc.
- LibMNG © 2000-2001 Gerard Juyn
- Gif-RLE © Hutchison Avenue Software Corporation, 1998
- LibJ2K © David Janssens, 2001-2002
- LibJBG © Markus Kuhn, 2002
- JasPer © Image Power, UBC, Michael David Adams, 2001-2003
- zlib © 1995-2003 Jean-loup Gailly and Mark Adler
Wood and stone textures obtained from
http://www.mayang.com/textures
Hopefully you'll be able to work the rest of the interface out on your own!
There are lots of menus to look through. Let me know if you have any problems
or can't figure out how to do something. I'll be interested to hear what you
think!
Copyright © 2001-2025, Robert Webb
Stella Home Page:
http://www.software3d.com/Stella.php