Compounds of Cubes & Tetrahedra

[marcelteun]

I understand that it is not straightforward to create compounds in Stella (I don't use Stella myself, yet). Therefore I thought that Stella users might be interested in the fact that I have some archives with off files available:

http://www.tunnissen.eu/polyh/Tetrahedr ... ds.off.zip
http://www.tunnissen.eu/polyh/CubeCompounds.Off.zip
http://www.tunnissen.eu/polyh/Octahedra ... ds.Off.zip

The following pages contain some more info about these compounds:
http://www.tunnissen.eu/polyh/tetrahedr ... .vrml.html
http://www.tunnissen.eu/polyh/cubecmps.vrml.html
http://www.tunnissen.eu/polyh/octacmps.vrml.html

Since I don't really use off files myself, errors might exist in these archives. Feed back is always welcome (even though I might be too busy with other things to fix any problems immediately)

/Marcel Tünnissen

[robertw]

Thanks Marcel!

I tried them, and the OFF files seem to open easily in Stella. along with their nets. All 357 could all be loaded, but Stella failed to create nets for 5 of them, claiming possible accuracy errors, but who knows. I'll have a look sometime and see if I can shed any light on it.

The easiest way to step through all these in Stella is to put all the OFF files in a single folder. Open one, and then just use the Right arrow to step through them all one by one

Most are multi-coloured, but I found one compound of cubes with only a single colour: 12.A4xI.ExI.off. In Stella it is easy enough to recolour them with different colours for each component in the compound. Just hit Shift+A (Menu: Color->Color as a Compound). Oh, this one with octahedra is also a single colour: 24.S4xI.ExI.off.

This compound of tetrahedra has an error: A5xI_C3_40.eg.off. It is supposed to be a compound of 40 tetrahedra, but instead there are 60, with the extra 20 being coincident with half of the existing 40. S4xI_D2C2_12.off shows a similar problem.

Hey, I wouldn't like trying to make this one from paper: 30A.A5xI.C2xI.mu5.1col.off!

Rob.

[marcelteun]

Thanks for your feed back Rob!
I put a new file with compounds of tetrahedra there with new versions of A5xI_C3_40.eg.off. and S4xI_D2C2_12.off. After I regenerated the zip file I noticed it contained 8 files more than before. I didn't check which files were extra.

Btw the archive does not contain any special positions for the compounds with rotational freedom, since I was not ready with them.

[robertw]

I noticed it contained 8 files more than before. I didn't check which files were extra.

Don't know what it means, but here are the extra files:
C6_E_6.eg.off
D12xI_C3_16.eg.off
D18D9_D3C3_6.off
D1xI_C2C1_2.eg.off
D2D1_D1C1_2.eg.off
D6_E_12.eg.off
D6C6_E_12.eg.off
D9xI_C3_12.eg.off

Mean anything to you?
Rob.

[marcelteun]

C6_E_6.eg.off
...
Mean anything to you?

Sure, it was me who named all of them (but it was a while ago that I worked with this set and apparently I didn't have the last version on my site before)
The names are derived from Verheyen's notation, with the difference that I move the amount to the end of the name. The mapping is as follows:

Code: Select all

nr | G / F   -> G_F_nr.off

For compounds with central or rotational freedom I just give an general example and then the name ends with .eg.off. The reason that I moved the nr of constituents to the end is that sorting on symmetry group gives a better order than sorting on the amount of constituents imho.

So C6_E_6.eg.off is a compound of 6 with a six fold cyclic symmetry with central freedom, ie. every symmetry operation of the symmetry group except E maps a constituent on another one. Verheyen's notation would be 6 | C6 / E and this is another example of n | Cn / E beside the 4 | C4 / E that was already in the previous archive.

[marcelteun]

Last monday I was sick: I was lying in bed staring at my models of compounds of cubes and my mind wandered off. I thought that there should be a compound of containing 5 times a compound of six cubes (6 | S4 x I / D2 x I).

Yesterday evening (I felt much better then) I tried it and found myself looking at a compound that I seen before: 30A | A5 x I / C2 x I | mu_10
with mu_10 = pi/4
Veheyen's book "Symmetry Orbits" specifies that this compound consists of 15 x 2 | D4 x I / D2 x I
Apparently it is even more special.
It actually consists 5 x 6 | S4 x I / D2 x I

Nothing new really, but nice to know that even sickness has its advantages.


(I can post a picture later)

[Gronkling]

You can make octahedral and tetrahedral archimedian compounds from these by morph duals (Usually truncation). You can also facet them to make other uniform solids but its quite hard on complex polyhedra. (You probably already knew this but I just wanted to say )

[jos smits]

Hallo Marcel ! Many thanks for all the wonderful compounds you made. I wonder how you did it.... I opened them simply the way Robert suggested and had a hell of a good time after. Why not try a few a few more. Dodecah. Icosah...... Dankjewel. Jos.

[marcelteun]

The following pages contain some more info about these compounds:
http://www.tunnissen.eu/polyh/tetrahedr ... .vrml.html
http://www.tunnissen.eu/polyh/cubecmps.vrml.html
http://www.tunnissen.eu/polyh/octacmps.vrml.html

Since VRML is hopelessly outdated, I also have pages that use Javascript to show the models. So far I only did the Cubes and Octahedra. And the ones with rotational freedom just show an example, nothing fancy with a slide-bar, but now I can show interactive 3D models of the compounds even in my phone:
http://tunnissen.eu/polyh/cubecmps.html
http://tunnissen.eu/polyh/octahedron_co ... index.html