Polyhedron with twelve pentagonal faces with five pentagons meeting at each vertex, intersecting each other making a pentagrammic path. It has thirty edges and twelve vertices. It is a Kepler-Poinsot polyhedron, one of the four non-convex regular polyhedra.

The surface area of a great dodecahedron with edge length a is given by the formula:

The volume of a great dodecahedron with edge length a is given by the formula: