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
12 (number) is a subset of 12's proper divisors that add up to 12 (all of them but with 4 excluded), 12 is a semiperfect number. If an odd perfect number is of the form 12"k" + 1, it has at least twelve distinct prime factors. A twelve-sided polygon is a dodecagon. A twelve-faced polyhedron is a dodecahedron. Regular cubes and octahedrons both have 12 edges, while regular icosahedrons have 12 vertices. Twelve is a pentagonal number. The densest three-dimensional lattice sphere packing has each sphere touching 12 others, and this is almost certainly true for "any" arrangement of spheres (the Kepler