Disphenoid tetrahedra

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relwes
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Joined: Mon Oct 15, 2018 9:09 pm

Disphenoid tetrahedra

Post by relwes » Mon Oct 15, 2018 9:15 pm

Hello - I'm having lots of fun with Stella4d - a tremendous bit of kit.

Disphenoid tetrahedra (aka sphenoids) - i.e. tetrahedra whose faces are non-equilateral triangles - are interesting as they are the only irregular convex noble solids (i.e. isohedral and isogonal but not - at least in this case - isotoxal). See page 15 here: https://sites.math.washington.edu/~grun ... yhedra.pdf

Can you think of some way to create them in Stella? If not, that is my suggestion for a future update!

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robertw
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Re: Disphenoid tetrahedra

Post by robertw » Tue Oct 16, 2018 2:25 am

How would one define a disphenoid in general?

You can find most of Bruckner's noble polyhedra in Stella in "Stella Library->Bruckner". Many of these are actually compounds, and quite a few are compounds of disphenoids. So you could isolate one of those from the compound. And generally, you could use faceting mode to make many disphenoids from other polyhedra.

By the way, did you see the new noble polyhedron I discovered? Apparently the first one found for about a century.
https://www.software3d.com/NobleSnub.php
Image

There are some others than can be easily found with Stella.

relwes
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Joined: Mon Oct 15, 2018 9:09 pm

Re: Disphenoid tetrahedra

Post by relwes » Tue Oct 16, 2018 6:18 am

Marvellous - thanks!

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