# The Icosidodecahedron

A semi-regular polyhedron with two triangles and two pentagons alternating around each vertex.

The icosidodecahedron is one of the thirteen archimedian solids. It can be created by slicing suitable sections off the vertices of either a dodecahedron or an icosahedron and thus may be inscribed in either solid.

 VertexSymbol WythoffSymbol No. ofVertices No. ofEdges {3}Faces {5}Faces SymmetryGroup Dual Polyhedron 3.5.3.5 2 | 3 5 30 60 20 12 A5×C2 RhombicTriacontahedron

Edge ratios:

• e/rho = 2tan(18^@)=2sqrt((5-2sqrt(5))/5)
• e/R = (sqrt(5)-1)/2
• e/(e_12) = (1+sqrt(5))/4
• e/(e_20) = 1/2

where e is the edge length, rho is the inter-radius, R is the circum-radius, e_12 is the edge of the circumscribing dodecahedron, and e_20 is the edge of the circumscribing icosahedron.