# The Great Dodecahedron

A non-convex polyhedron bounded by twelve intersecting pentagonal faces. It has twelve '5/2' star vertices.

The great dodecahedron is one of the four Kepler-Poinsot Star Polyhedra, and is also the second stellation of the dodecahedron.

 VertexSymbol WythoffSymbol No. ofVertices No. ofEdges No. ofFaces SymmetryGroup Dual Polyhedron (5)5/2 5/2 | 2 5 12 30 12 A5×C2 Small StellatedDodecahedron

Edge ratios:

• e/r = sqrt(10-2sqrt(5))
• e/rho = sqrt(5)-1
• e/R = sqrt( (10-2sqrt(5))/(5) )
• e/e_(12) = (1+sqrt(5))/2

where e is the edge length, r is the in-radius, rho is the inter-radius, R is the circum-radius, and e_(12) is the edge of the inner dodecahedron.