A cube is a solid figure contained by six equal squares.

An octahedron is a solid figure contained by eight equal and equilateral triangles.

An icosahedron is a solid figure contained by twenty equal and equilateral triangles.

A dodecahedron is a solid figure contained by twelve equal, equilateral and equiangular pentagons.

These are four of the five regular solids. The tetrahedron is not mentioned here since it is a certain triangular pyramid. It’s called simply the “pyramid” in Book XIII.
The regular tetrahedron is constructed in proposition XIII.13, the cube in XIII.15, the octahedron in XIII.14, the icosahedron in XIII.16, and the dodecahedron in XIII.17. These five are shown to be the only regular solids in proposition XIII.18. |