# The Great Icosahedron

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

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

 VertexSymbol WythoffSymbol No. ofVertices No. ofEdges No. ofFaces SymmetryGroup Dual Polyhedron 35/2 5/2 | 2 3 12 30 20 A5×C2 Great StellatedDodecahedron

Edge ratios:

• e/r = sqrt(10+2sqrt(5))
• e/rho = 1 + sqrt(5)
• e/R = sqrt( (10+2sqrt(5))/5 )
• e/e_(20) = (7+3sqrt(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_(20) is the edge of the inner icosahedron.