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 ratio rectangles of ratio ("ϕ" + 1) : 1 and "ϕ" : 1 also fit perfectly within a regular dodecahedron. In proportion to this golden rectangle, an enclosed cube's edge is "ϕ", when the long length of the rectangle is "ϕ" + 1 (or "ϕ") and the short length is 1 (the edge shared with the regular dodecahedron). In addition, the center of each face of the regular dodecahedron form three intersecting golden rectangles. It can be projected to 3D from the 6-dimensional 6-demicube using the same basis vectors that form the hull of the rhombic triacontahedron from the 6-cube.