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Images may be put on faces of polyhedra, and will appear on nets when
printed out. Images may be mapped individually on each face, as in first image
below, or projected through the model linearly, cylindrically, or spherically
as seen in the other images below. The first image below also shows spheres at
the vertices and cylinders along the edges, with golden spheres and wooden
edges.
Small Stella, Great Stella and Stella4D can all display the rotational and reflective symmetries of any polyhedron.  
Now you can select a rotational symmetry axis and pivot around it.  
Stella has customisable animated transitions between models.  
Stella allows you to create polyhedral slideshows called tours. Each event may be animated (rotating, morphing, unfolding, slicing), with animated transitions between each. This animation goes for 30 seconds. Watch full 80 second version with commentary on YouTube below: 

Here we see crosssections of various polyhedra. The animation comes from moving the slicing plane through the model over time, and can be shown in realtime within the software (Small Stella, Great Stella or Stella4D). Top left shows crosssections embedded in the cube. This helps to show how these slices fit into the original model. Can you tell which polyhedra are being sliced in the other images? 
A screenshot from the Demo version of Great Stella. This shows the Rainbow colouring mode, and the fact that the icosahedron may be stellated in the Demo version.  
This is a screenshot from Great Stella, showing the stellation diagram attached to the face of a 3D model (the icosahedron). The lines indicate where other face planes intersect with this one. You can click on a 2D region of the diagram to enable the 3D cell behind that region, as shown here.  
In Great Stella, use this toolbar button to enter "Create Facets Mode"...  
...then use Shift+Leftclick on the vertices of the facets you want, which will become faces of a new model when you use "Poly→Create Faceted Polyhedron". In this example we create a compound of 15 cuboids. Only three facets need to be created manually because they will be repeated over the symmetry group to create the complete set of faces. Finally we colour them in orthogonal sets of three using "Color→Special Color Arrangements→Rhombic Triacontahedral Arr 1 (5 colors)".  
Or, let Great Stella find facetings for you. You can step through valid facetings, according to the criteria you've selected, using the Up arrow in the Faceting Preview view. Here are the facetings of the icosahedron).  
In Great Stella you can create a zonohedron or zonish polyhedron based on any other polyhedron. Here is a zonish polyhedron. Created as follows: start with an icosidodecahedron, use "Poly→Zonohedrify", select "Add zones to existing faces" at top, and tick only "All faces" in the middle section.  
This screenshot is from Small Stella (and would also be available in Great Stella and Stella4D of course). It shows a singleview layout, with 3D stereo enabled. You need to wear redblue or redgreen glasses to view this image properly. Click on the image for a full size version.  
This screenshot is from Great Stella. It shows a fiveview layout. The only view here that wouldn't be available in Small Stella is the one in the bottom right corner, which shows the stellation diagram for the great icosahedron in the big view. The model itself is available in Small Stella. Click image to see it full size.  
Another screenshot from Great Stella, showing the small inverted retrosnub icosicosidodecahedron (aka Yog Sothoth). This model is only available in Great Stella and Stella4D. Click image to see it full size.  
This shows the augmentation feature of Great Stella. You can augment any model with any other model. Here a pentagonal pyramid (J2) is being augmented with a square pyramid (J1) at one of the triangular faces. The user sees a preview of the result and can cycle through the possible orientations before choosing the one they want.  
Measurement mode allows you to measure distance and angles between points, lines, planes, and in Stella4D, cells.  
Overlapping coplanar faces have their colours blended in realtime. 
Formatted text may be places on faces, edges and vertices. Some limited HTML markup is recognised in order to format and colour the text. You may even have links in your text! Link to websites, email, or to open other models in Stella.  
Formatted text on faces is also printed on nets. Make your own polyhedral dice. 
Below are animations showing views where a polyhedron can be morphed into
its dual. Each shows a different model, and uses a different method for doing
the transformation. In the software, the transformation is controlled
interactively with the mouse. See
my paper for a description of
some of these techniques.
Enable Geomag mode to render models as if they were constructed using the Geomag magnetic construction kit.
Geomag Icosadodecahedron 
Geomag rocket  Geomag picture frame  Geomag castle 
Screenshot from Stella4D (click image for fullsize version). Shows the uniform polychoron Thi, whose cells are 120 truncated dodecahedra and 600 tetrahedra. The smaller views show a crosssection, net, dual, and vertex figure.  
Screenshot from Stella4D (click image for fullsize version). Shows the regular polychoron Gaghi, whose cells are 120 great dodecahedra. The main window shows a 3D crosssection of the polytope. 
Here is the best known polychoron and probably the simplest to understand. It is the tesseract, also known as the 8cell or 4D cube. It has eight cubes as its cells (or sides). Here it is shown with all the cells hidden, leaving just the edges and vertices visible. It has been projected into 3D so that we may view it in our world, just as a 3D model is projected into 2D when we view it on a computer screen.  
Getting a bit more complicated, here is a cantitruncated tesseract (uniform polychoron number 308, aka "grit", in Stella4D). This polytope has 56 cells. 32 truncated cuboctahedra (hidden), 16 truncated tetrahedra (yellow), and 8 triangular prisms (red). Again, it has been projected into 3D, this time with only the truncated cuboctahedral cells hidden. See my paper model here.  
 Each "side" of a 4D polytope is a 3D polyhedron, just as each side of a 3D polyhedron is a 2D polygon; and just as in 3D, you can unfold the sides into a "flat" net. I put "flat" in quotes because here flat means that the unfolded cells lose their fourdimensionality, being reduced to 3D. Here you see two such nets. The first for the truncated tesseract (19Tat in Stella4D. See my paper model). The second is for the dual of another uniform polychoron (20Thex). 
Nets for more complex polychora get quite impressive. Here is the net for the cantellated 120cell (158Srahi in Stella4D). 
3D perspective projection of the 120cell, a regular 4D polytope with 120 regular dodecahedra for its sides. 
Net for a 7,2 gyrochoron. Gyrochora are duals of step prisms, so use "4D→Create 4D Step Prism" in Stella4D, enter "7 2" when prompted, and look at the net of the dual to find this model. 
Here is the tesseract rotating in 4D before being projected into 3D. Stella4D lets you rotate like this interactively.  
The tesseract again, with a cellfirst crosssection passing through it. The crosssection itself doesn't change, remaining a cube throughout, but appears to distort due to the projection from 4D into 3D. Stella4D lets you interactively change the slicing depth with the mouse.  
This time it's a vertexfirst crosssection, which starts as a growing tetrahedron, gets truncated towards an octahedron, then extends out the other way back into a tetrahedron. Again, it appears distorted throughout due to the perspective projection from 4D into 3D.  
Here are crosssections of the 600cell, which has 600 tetrahedra as its sides. Not embedded in the original 4D model here, so no distortion this time.  
Crosssection of a 4D Waterman polychoron.  
Getting more complex now, and this is still just a regular polychoron! Here we see crosssections of the great grand stellated 120cell (16Gogishi in Stella4D), which has 120 great stellated dodecahedra as its cells.  
Crosssections of another regular polychoron, the great stellated 120cell (12Gishi in Stella4D), which again has 120 great stellated dodecahedra as its cells. I have made two of these crosssections as paper models here and here. 
Here's a crosssection of the grand 600cell (15Gax in Stella4D), which has 600 tetrahedra as its cells. 
Here you see the 120cell (5Hi in Stella4D)
projected into 3D. Most cells have been hidden, with just two rings of
dodecahedra remaining.
Colour Mode makes it easy to recolour
each cell in a ring like this, then you can hide all the remaining cells of the
original colour in one hit.
Update: I have now made this model from paper, adding one extra cell to hold the two rings in place. 
Two methods are available for morphing between 4D polytopes and their duals. 
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