# The Small Stellated Dodecahedron

A non-convex polyhedron bounded by twelve intersecting pentagrams; five meeting at each vertex.

The small stellated dodecahecahedron is one of the four Kepler-Poinsot Star Polyhedra, and is also the first stellation of the dodecahedron.

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

Edge ratios:

• e/r = sqrt(10+2sqrt(5))
• e/rho = 1 + sqrt(5)
• e/R = sqrt( (10+2sqrt(5))/(5) )
• e/e_(12) = (3+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.