Dodecahedron

A dodecahedron

A dodecahedron is a polyhedron (a three-dimensional shape) that has 12 faces. Each face is a pentagon (a polygon with five edges). It has 20 corners (also called vertices) and 30 edges altogether.

A regular dodecahedron, which looks exactly the same from all faces, is a Platonic solid. The dual of a dodecahedron is an icosahedron.

Surface area and volume

If a is the length of one of its edges, the surface area and volume of a regular dodecahedron are:

$A=3{\sqrt {25+10{\sqrt {5}}}}a^{2}$

$V={\frac {15+7{\sqrt {5}}}{4}}a^{3}$