Posted: Dec 20, 2012 11:06 pm
tuco wrote:To be isohedral, each face must have the same relationship with all other faces, and each face must have the same relationship with the center of gravity. - http://www.mathpuzzle.com/Fairdice.htm
This makes sense, and can, in limited fashion, be observed when playing with toys as a kid. So how many possible there are?
I had listed them, and there are 2 infinite families and 18 quasi-spherical ones (Platonic and Catalan solids). If one uses only the equatorial belts of prisms and antiprisms, one gets 2 more infinite families.