Re: [math-fun] Can a polyhedron

"R. William Gosper" wrote:

with its vertices on a sphere and its edge lengths all equal have more than 92 faces? I'm looking at one (a doenneacontahedron?) with 12 regular pentagons (pentaga?), 60 equilateral triangles, and 20 non-regular (but equilateral) hexagons. There are 90 vertices, all tetravalent, so maybe there is a C_90 fullerane (as opposed to fullerene).

A polyhedron has planar faces. If it is inscribable, the vertices of a given face lie on the circle where the plane intersects the sphere. So how can you have a non-regular equilateral hexagon inscribed in a circle? George http://www.georgehart.com/