Truncated dodecahedron Truncated dodecahedron In geometry, the truncated dodecahedron is an Archimedean solid. It has 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges. This polyhedron can be formed from a dodecahedron by truncating (cutting off) the corners so the pentagon faces become decagons and the corners become triangles. It is used in the cell-transitive hyperbolic space-filling tessellation, the bitruncated icosahedral honeycomb. The area "A" and the volume "V" of a truncated dodecahedron of edge length "a" are: Cartesian coordinates for the vertices of a truncated dodecahedron with edge length 2"φ" − 2, centered at the origin, are
Regular dodecahedron faces) is while the midradius, which touches the middle of each edge, is These quantities may also be expressed as where "ϕ" is the golden ratio. Note that, given a regular dodecahedron of edge length one, "r" is the radius of a circumscribing sphere about a cube of edge length "ϕ", and "r" is the apothem of a regular pentagon of edge length "ϕ". The surface area "A" and the volume "V" of a regular dodecahedron of edge length "a" are: Additionally, the surface area and volume of a regular dodecahedron are related to the golden ratio. A dodecahedron with