Return to Revisions

Not too sure I fully understand.

I think the idea is filling triangular faces with smaller triangles, 6 along each edge (example used in the wiki)

So creating a 2D approximation, flattening out the icosahedron we get a net of 20 triangular faces, 10 squares in a 5x5 box

we can get the pattern in 2D

Then wrap it around a sphere (using the code from this post)

You can adjust the shape for truncated icosahedron. Or are you are looking for a manipulation in 3D?

For some reason SpherePoints[] is removed from my mathematica, however

Graphics3D[Line[SpherePoints[100]]] 

if you combine this and some form of ShortestPath

SpherePoints[100]; Graphics3D[Line[%[[Last[FindShortestTour[%]]]] 

if you set the number of points to that of the number of points on the sphere they should be evenly spaced and the same effect.