Truncated Icosahedron Tile Objects

Question

I'm trying to make a truncated icosahedron, though with more subdivision (so more hexagons) In the game I use it, eacht pentagon and hexagon is a separate object. So after generating the icosahedron, I just use the generated points to place either a pentagon or a hexagon on it (instead of doing the find-middles-of-each-triangle-thing, I do this since I need them to be separate object anyway.) I have some questions about it though, and google doesn't really help, so I'm hoping there are some smart smath-knowing people here :D

Here we go:

1. Am I assured that the length of each sides is equal?
2. Since each hexa/petagon is a separate object, I need to rotate them to get them positioned properly, any help with this?
3. Assuming I have hexa/petagons with a radius of 1 (one), how far for the middle do I have to position them? (Basecly, whats the relationship between the radius of my hexa/pentagons and the radius of my truncated icosahedron.)

Here's my first test, I generated a icosahedron and then on each point put a pentagon model, which I rotate so it's pointing away from the middle. As you can see they still need to be rotated to fit together (question 2) and their distance to the middle has to the tweaked aswell (question 3).

I'll continue on working on this too, though all help will be appreciated! (I'm making this in Unity, using c#, so if you give sample code, it would be really really awesome if you use that.)

Thanks a lot!

Answer 1

Well, not the answer to your questions but maybe worth thinking about:

Wouldn't it be easier to start with a ready made Blender, Maya, ... model of a soccer ball like for example this one on Blend Swap, change it to fit your needs. Or do it on your own as there are a couple of YouTube tutorials. Then you will have far more options like LOD, materials. You can design it in Blender with each pentagon/hexagon as single object and so it will be imported in Unity.