Since Plato’s work, two other classes of equilateral convex polyhedra, as the collective of these shapes are called, have been found: Archimedean solids (including truncated icosahedron) and ...

ABHISHEK BHATTACHARYA, DAVID B. DUNSON, Nonparametric Bayesian density estimation on manifolds with applications to planar shapes, Biometrika, Vol. 97, No. 4 (DECEMBER 2010), pp. 851-865 ...

Platonic solids, the first class of such shapes, are well known. They consist of five different shapes: tetrahedron, cube, octahedron, dodecahedron and icosahedron.