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In geometry, the great stellated dodecahedron is a Kepler-Poinsot solid. It is one of four non-convex regular polyhedra.
It is composed of 12 pentagrammic faces, with three pentagrams meeting at each vertex.
The 20 vertices match the vertices of a dodecahedron.
Shaving the triangular pyramids off results in an icosahedron.
It is counted by Wenninger as model * and the third and last stellation of the dodecahedron.
If the pentagrammic faces are broken into triangles, it is topologically related to the triakis icosahedron, with the same face connectivity, but much taller isosceles triangle faces.
"Great stellated dodecahedron"