Polyhedron with twenty intersecting triangular faces with five triangles meeting at each vertex in a pentagrammic sequence. 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 icosahedron with edge length $a$ is given by the formula:

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