Dodecahedron pentagonal faces, with three meeting in each of the 20 vertices. However, the pentagons are not regular and the figure has no fivefold symmetry axes. Although regular dodecahedra do not exist in crystals, the tetartoid form does. The name tetartoid comes from the Greek root for one-fourth because it has one fourth of full octahedral symmetry, and half of pyritohedral symmetry. The mineral cobaltite can have this symmetry form. Its topology can be as a cube with square faces bisected into 2 rectangles like the pyritohedron, and then the bisection lines are slanted retaining 3-fold rotation at the 8 corners.
Truncated dodecahedron straight edges. It shares its vertex arrangement with three nonconvex uniform polyhedra: It is part of a truncation process between a dodecahedron and icosahedron: This polyhedron is topologically related as a part of sequence of uniform truncated polyhedra with vertex configurations (3.2"n".2"n"), and ["n",3] Coxeter group symmetry. In the mathematical field of graph theory, a truncated dodecahedral graph is the graph of vertices and edges of the "truncated dodecahedron", one of the Archimedean solids. It has 60 vertices and 90 edges, and is a cubic Archimedean graph. Truncated dodecahedron In geometry, the truncated dodecahedron is an Archimedean solid. It has