Inspired by this post: Floret Tessellation of a Sphere I tried to transform myself an icosahedron into its simplest Floret tessellation. But I am having trouble when applying the 'method' given in the referenced post.
Here's what I do:
- Start with a regular icosahedron.
- Replace each triangle face with 3 pentagons (still coplanar to the original icosahedron face).
- Push the new vertex onto the bounding sphere (that of the original icosahedron).
You can see on the following render these 3 steps.
My problem is, after step 3, I have gaps in my model. They're barely visible on the picture, but there are gaps, the new vertices don't match exactly after being pushed, and the pentagons are not flat either. So in the end this is not a "Pentagonal hexecontahedron", and not even a polyhedron.
I guess the vertex pushing part might be causing this, as I'm not sure the new vertex should be pushed onto the same bounding sphere as the icosahedron's.
So can I really build a Pentagonal hexecontahedron this way?