# The Truncated Icosahedron

A semi-regular polyhedron with two hexagons and a pentagon meeting at each vertex.

The truncated icosahedron 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 {5}Faces {6}Faces SymmetryGroup Dual Polyhedron 5.6.6 2 5 | 3 60 90 12 20 A5×C2 Pentakis Dodecahedron

Edge ratios:

• e/rho = (sqrt(5)-1)/3
• e/R = sqrt((58-18sqrt(5))/109)
• e/(e_12) = (7+5sqrt(5))/38
• e/(e_20) = 1/3

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.