Equilateral pyramids from base triangles

Hello everyone!
I have the following set of curves, they all form equilateral triangles on a sphere. The way I constructed them is I used the MeshIcoSphere plugin and then used Kangaroo to get all the curves to be the same length.
What I want now is to each of this triangles to be the base of a pyramid. Can anyone point me in the right direction?
Thank you very much!


icosaedro.gh (4.4 KB)
icosaedro.3dm (7.2 MB)

The weaverbird plugin has a component called “stellate” that will accomplish this effect. Looks like you have it installed.

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I’ll check it out, thank you!

This isn’t possible.
You’re seeing the same value repeated a few dozen times just because of the edge ordering from the subdivision. Scroll down your list further and you’ll see the other lengths are different.

You can make the edge lengths all equal, but the result isn’t a smooth sphere, instead something crumpled like this:

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welp, you are right!
Can I do it with any shape? a square? an hexagon? non equilateral triangles?

You can cover a sphere with 120 identical (up to reflection) triangles like this

For more faces they’d need to be different shapes

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Wait, are there more of these irregular large polyhedra formed by equilateral triangles?

All along I’d been thinking of the icosahedron’s status as the biggest platonic solid as a limit, when in fact it appears there’s a world of opportunity?

Yes, if you don’t require them to be convex, then there are infinite polyhedra of only equilateral triangles possible. If you search for Lobel frames there are a few discussions on here and the old gh forum.

3 Likes

Thanks!