An "icosphere" has the mathematical name geodesic polyhedron. It's an approximation to a sphere made out of triangles with either 5 or 6 triangles meeting at a vertex. It can be made by a subdivision of a dodecahedron into triangles. The number of subdivisions determines what type of icosphere you have.
My question:
Do the triangles in an icosphere all have the same solid angle from the center?
I expect that all triangles on a 6-vertex are equivalent and that all triangles on a 5-vertex are all equivalent, so I can't see that they would be the same.
If they are different, is there a way to know the solid angle for any given size icosphere?
