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.
Great dodecahedron pentagram, its two-dimensional analogue, via the extension of the ("n-1")-D pentagonal polytope faces of the core "n"D polytope (pentagons for the great dodecahedron, and line segments for the pentagram) until the figure again closes. It shares the same edge arrangement as the convex regular icosahedron; the compound with both is the small complex icosidodecahedron. If only the visible surface is considered, it has the same topology as a triakis icosahedron with concave pyramids rather than convex ones. The excavated dodecahedron can be seen as the same process applied to a regular dodecahedron. A truncation process applied to the great dodecahedron