The cube can also be called a regular hexahedron and is one of the five Platonic solids.

A cube, for example, is a regular hexahedron with all its faces square, and three squares around each vertex.

Cube (regular hexahedron)

The "hemi" part of the name means some of the faces form a group with half as many members as some regular polyhedron-here, three square faces form a group with half as many faces as the regular hexahedron, better known as the cube-hence hemihexahedron.

A regular icosahedron with identical equilateral faces is often meant because of its geometrical significance as one of the five Platonic solids, all regular polyhedrons including the regular tetrahedron, the cube or regular hexahedron, the regular octahedron, and the regular dodecahedron with 4, 6, 8 and 12 identical faces, respectively.