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
Bilinski dodecahedron of lengths of the two diagonals is the golden ratio; that is, the faces of this shape are golden rhombi. In contrast, for the standard rhombic dodecahedron the corresponding ratio is the square root of 2. This shape is a zonohedron. Like the rhombic dodecahedron, it can tile three-dimensional space by translation, making it a parallelohedron. The Bilinski dodecahedron and rhombic dodecahedron have the same topology: their vertices, edges, and faces correspond one-for-one, in an adjacency-preserving way. However, their geometry is different. In a 1962 paper, H. S. M. Coxeter claimed that the Bilinski dodecahedron could be obtained by an