Polyhedron with twelve pentagrammic faces with three pentagrams meeting at each vertex. It has thirty edges and twenty vertices. It is a Kepler-Poinsot polyhedron, one of the four non-convex regular polyhedra.

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

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