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.
Snub dodecahedron of snubbed polyhedra and tilings with vertex figure (3.3.3.3."n") and Coxeter–Dynkin diagram . These figures and their duals have ("n"32) rotational symmetry, being in the Euclidean plane for "n" = 6, and hyperbolic plane for any higher "n". The series can be considered to begin with "n" = 2, with one set of faces degenerated into digons. In the mathematical field of graph theory, a snub dodecahedral graph is the graph of vertices and edges of the snub dodecahedron, one of the Archimedean solids. It has 60 vertices and 150 edges, and is an Archimedean graph. Snub dodecahedron In geometry,