Great dodecahedron

The great dodecahedron, or gad, is one of the four Kepler–Poinsot solids. It has 12 pentagons as faces, joining 5 to a vertex in a pentagrammic fashion.

It is in the same regiment as the icosahedron, and comes from using the icosahedron's vertex figure pentagons as the faces.

It is the second stellation of the dodecahedron.

Great dodecahedra appear as cells in two star regular polychora, namely the great hecatonicosachoron and great grand hecatonicosachoron.

Vertex coordinates
Its vertices are the same as those of its regiment colonel, the icosahedron.

In vertex figures
The great dodecahedron appears as a vertex figure of two Schläfli–Hess polychora.

Related polyhedra
Abstractly the great dodecahedron is a quotient of the order-5 pentagonal tiling. Specifically it is $$\{5,5\mid 3\}$$, a tessellation of Bring's surface. It is also abstractly equivalent to its conjugate, the small stellated dodecahedron.

Two uniform polyhedron compounds are composed of great dodecahedra:


 * Pentagonal retrosnub pseudodisoctahedron (2)
 * Pentagonal retrosnub pseudicosicosahedron (5)