A Platonic solid is a geometric shape made of only one type of regular polygon. There are only five Platonic solids.

The names come from the Greek words for the number of faces plus “εδρον” (“edron”) meaning seat or face.

They are related to the Archimedean solids.

Tetrahedron | Hexahedron aka Cube |
Octahedron | Dodecahedron | Icosahedron | |
---|---|---|---|---|---|

Faces | 4 | 6 | 8 | 12 | 20 |

Edges | 6 | 12 | 12 | 30 | 30 |

Vertices | 4 | 8 | 6 | 20 | 12 |

The cube and octahedron are duals of each other, as are the dodecahedron and icosahedron. The tetrahedron is its own dual.

Since each face is equal to each other face, the platonic solids are often used for dice shape, referred simply by their face count, D4, D6 (most common), D8, D12, D20.