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 ā€œstellateā€ that will accomplish this effect. Looks like you have it installed.

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Iā€™ll check it out, thank you!

This isnā€™t possible.
Youā€™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 youā€™ll see the other lengths are different.

You can make the edge lengths all equal, but the result isnā€™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 theyā€™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 Iā€™d been thinking of the icosahedronā€™s status as the biggest platonic solid as a limit, when in fact it appears thereā€™s a world of opportunity?

Yes, if you donā€™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.

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Thanks!