How can I build an array of coordinates of a truncated icosahedron's faces?

Question

I can easily get a list of coordinates of all the vertices—the Wikipedia page has formulae and this page has a list of them, but that doesn't tell me which ones are part of which face.

What I'd like is to create an array of 32 faces, and for each one have:

• The 3-coordinate of the center of the face
• The rotation of the face about the center point
• Whether it's a pentagon or a hexagon

How can I generate that data?

Answer 1

I'd suggest you use Blender. It's easy to get the information you want for any geometric object you create, using python scripts. It's free, easy to use and you can get extensive support online.

1) download Blender here: https://www.blender.org/download/ (it's free)

2) Check this question, first answer, to create easily a truncated icosahedron https://blender.stackexchange.com/questions/31727/truncated-icosahedron

3) Go to "Objects mode" and select your geometry (right mouse button).

4) Open the python console by pressing Shift-F4. Copy and paste this script:

import bpy, bmesh
obj = bpy.context.active_object
verts = [vert.co.to_tuple() for vert in obj.data.vertices]
faces = [ [ vertex for vertex in face.vertices ] for face in obj.data.polygons]

Now verts is a list of the coordinates of all the vertices, and faces is a list of all the faces. Each face is a list of indices referencing to the verts list. You can inspect them using print verts and print faces. I would suggest you save them to a file, using numpy for example.