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Isohedron : A convex polyhedron with symmetries acting transitively on its faces. Every isohedron has an even number of faces (Grьnbaum 1960). The isohedra make fair dice, and there are 30 of them, many of which are Platonic solids, Archimedean solids, or duals of Archimedean solids.

The 30 isohedra are the cube, disdyakis dodecahedron, deltoidal hexecontahedron, deltoidal icositetrahedron, disdyakis triacontahedron, dodecahedron, dyakis dodecahedron, hexakis tetrahedron, icosahedron, isosceles tetrahedron, octahedral pentagonal dodecahedron, octahedron, pentagonal hexecontahedron, pentagonal icositetrahedron, pentakis dodecahedron, rhombic dodecahedron, rhombic triacontahedron, scalene tetrahedron, tetragonal pentagonal dodecahedron, tetrahedron, tetrakis hexahedron, trapezoidal dihedron, trapezoidal dihedron (skewed), trapezoidal dodecahedron, triakis icosahedron, triakis octahedron, triakis tetrahedron, triangular dihedron, triangular dihedron (skewed in-out), triangular dihedron (skewed up-down).
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