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 The dodecahedra alone make a lattice of edge-to-edge pyritohedra. The bilunabirotundae fill the rhombic gaps. Each cube meets six bilunabirotundae in three orientations. The regular dodecahedron is topologically related to a series of tilings by vertex figure "n". The regular dodecahedron can be transformed by a truncation sequence into its dual, the icosahedron: The regular dodecahedron is a member of a sequence of otherwise non-uniform polyhedra and tilings, composed of pentagons with face configurations (V3.3.3.3."n"). (For "n" > 6, the sequence consists of tilings of the hyperbolic plane.) These face-transitive figures have ("n"32) rotational symmetry. The regular dodecahedron shares its