# The Truncated Dodecahedron

A semi-regular polyhedron with two decagons and a triangle meeting at each vetex.

The truncated dodecahedron 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 {10}Faces SymmetryGroup Dual Polyhedron 3.10.10 2 3 | 5 60 90 20 12 A5×C2 Triakis Icosahedron

Edge ratios:

• e/rho = (3sqrt(5)-5)/5
• e/R = sqrt((74-30sqrt(5))/61)
• e/(e_12) = sqrt(5)/5
• e/(e_20) = (3sqrt(5)-1)/22

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.