Can Anybody Help Me Make A Moravian Star Please?

[pollyhendra]

Hi, would love a hand with this one and perhaps a base to glue to might help as well. Thanks. (Moved better photo here, was trying to create more space in forum).

[robertw]

Hmm, it's hard to tell what shape it is, especially with the central part being washed out. It also quite possibly doesn't have as much symmetry as you might think, ie maybe only dihedral symmetry, not icosahedral or octahedral.

I think I'd need more info to replicate this one.

[guy]

I estimate around 48 points, by: counting all the points in its outline, adding all the visible points within its outline, then assuming that the same number are hidden round the back.

So it might well be the 50-point Moravian star - for hints on its construction, see for example http://en.wikipedia.org/wiki/Moravian_s ... s_of_Stars

First step is to truncate a great rhombicuboctahedron to create a 50-sided "core" solid. Can Stella do that easily?

Next step is to stellate the core.

[pollyhendra]

[robertw]

First step is to truncate a great rhombicuboctahedron to create a 50-sided "core" solid. Can Stella do that easily?

The one described on wiki truncates the RCO leaving octagons and hexagons. This model doesn't appear to have 8- or 6-sided peaks. But you could instead truncate all the way back to the edges' midpoints. One way to do that in Stella is to add the RCO to its dual and then take the convex core. Actually this seems to produce something very close to the original photo. See below.

Next step is to stellate the core.

You mean augment the core? I notice the wiki page makes the same mistake, referring to one start as a "great stellated" RCO, but it's faces do not lie in the RCO's facial planes, so it's not a stellation. Maybe I'll fix that and see who notices.

For my model below, I set the radius of the RCO to 1, then augmented each face type in turn with pyramids, with "Pyramid height" set to "Height = 1" and a scale of 3 for the squares, and 2 for the other faces. Tweak those scales for different results.

I'm not aware of any rules about how pointy Moravian stars should be, ie the height of the points. Being used as decorations I imagine there's not too many guidelines.

Sorry about photos. Hope these help.

These are photos of a different model, with only 26 points rather than 50. To make these ones, skip the truncation step. Just augment the faces of an RCO directly. See below. This time I used what is probably a more likely method: set the original edge length of the RCO to 1, and augment with pyramids with "New Edge Lengths = 1" and a scale of 4 for the squares and 3 for the triangles.

[guy]

Yes, you are right.

I think "rectify" may be the operation of blending the polyhedron with its dual, I can't remember if that is the right word. It certainly gives a more accurate model (and nicer) than truncation.

And yes it is augmentation not stellation. There might well be a convex core that can be stellated to give the correct result, but it will be a different polyhedron and not suitable as the model core.

[pollyhendra]

err um... Got the Archimedes model up. Now very simply, could you please give me a step by step for geometrically-challenged dummies?

[robertw]

Try following these steps:

• Probably want to close the net view while creating the model, so hit Ctrl+1 to get just one view (the base model view).
• Load a rhombicuboctahedron (File->Polyhedron List, type "RCO", hit Enter).
• Poly->Add Base Model and Dual
• Poly->Create Convex Core
• Probably want to do "Scale->Base Polyhedron Radius" to set the current size to something known, eg "1".
• Select the face you want to augment first (Shift+Left-click on it, or double-left-click).
• Hit "a" to augment (or "Poly->Augment Polyhedron" from the menu).
• A dialog appears. Choose the following options:
  • Select "Pyramid" if not already selected.
  • From the "Pyramid Height" drop-down, choose "Height = 1".
  • Set "Scale" to whatever height you want the pyramid peak, eg 3 or 2.
• Hit Enter (or click "OK"). A preview of the augmentation appears. Hit Enter again to accept it. Or hit "a" again to adjust the pyramid height etc if not as expected.
• Select another face and augment again until all faces have been augmented.

[pollyhendra]

Thanks for both helping. I'm currently finishing a model at the moment. Incidentlally, Rob, might pay to throw 'Moravian stars' into your keywords for Stella, as they are very popular and templates impossible to find. Thanks again.

[pollyhendra]

Quite happy with the 26, found the 50 a bit busy. Will continue to play around with this one, Thanks again.

[guy]

Congratulations.

When can we see the 50-arm star with interior lighting?

[pollyhendra]

Hey guy, fraid I left that one unfinished as I realised it was too busy. I will be tackling the 26 version again though - a breeze compared to the 50. I thought I'd like to leave a perimeter around the base of the augmentations though. Any idea how? Perhaps this picture will explain what I mean.

[Ulrich]

You can morph the rhombicuboctahedron to its dual by expansion up to say 20 %,
save it to the memory and retrieve it again. Then you do the augmentation of the
squares and the triangles:



Ulrich

[pollyhendra]

Terrific. Now for the geometrically challenged, that step by step goes....?

[Ulrich]

You load the Rhombicuboctahedron and click on the fifth icon from the right in
the last row (onmouseover you see "Morph Duals by Expansion"). Then you
keep the ctrl-button pressed, click the left mouse button and pull the mouse to
the right. Rectangles appear between the base model's faces and in the top
left edge of the window you see the degree of morphing. You stop the mouse
movement when it is at 20 %. To save this stadium you hit "m" and "1". To get
it back you hit "m" while the shift-button is pressed and click on memory 1.
Then you activate the base polyhedron view again and do the augmentation as
you did in your former model.

u.