A dodecahedron is a regular polyhedron, one of the five three-dimensional platonic solids, and has twelve congruent pentagonal faces. It has a schläfli symbol of , meaning that 3 pentagons join at each vertex. It is the dual of the icosahedron.
It is possible to inscribe 5 cubes into a dodecahedron such that all of the edges of the cubes are diagonals of the dodecahedron's faces.
It is also the only platonic solid to have pentagonal faces.
Subfacets and Structure
The dodecahedron has 12 pentagonal faces, joining three to a vertex. When seen face first, the layers start with one face, then the five surrounding it, then five more, and finally the opposite face.
|...||Trigonal hosohedron||Tetrahedron||Cube||Dodecahedron||Hexagonal tiling||Order-3 heptagonal tiling||Order-3 octagonal tiling||...||Order-3 apeirogonal tiling|
|...||Pentagonal dihedron||Dodecahedron||Order-4 pentagonal tiling||Order-5 pentagonal tiling||Order-6 pentagonal tiling||...||Infinite-order pentagonal tiling|
|Regular ||Rectified ||Birectified ||Truncated ||Bitruncated ||Cantellated ||Cantitruncated ||Dodecahedron||Icosidodecahedron||Icosahedron||Truncated dodecahedron||Truncated icosahedron||Rhombicosidodecahedron||Great rhombicosidodecahedron|