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In geometry, the great dodecahedron is a Kepler-Poinsot solid. It is one of four concave regular polyhedra.
It is composed of 12 pentagonal faces, with five pentagons meeting at each vertex, intersecting each other making a pentagrammic path.
The 12 vertices match the locations for an icosahedron.
This shape was the basis for the Rubik's Cube-like Alexander's Star puzzle.
Shaving off the concave part results in a dodecahedron.
It is considered the second of three stellations of the dodecahedron.
If the great dodecahedron is considered as a properly intersected surface geometry, it has the same topology as a triakis icosahedron with concave pyramids rather than convex ones.
"Great dodecahedron"