Excavated dodecahedron triangle is not present. The 20 vertices of the convex hull match the vertex arrangement of the dodecahedron. The faceting is a noble polyhedron. With six six-sided faces around each vertex, it is topologically equivalent to a quotient space of the hyperbolic order-6 hexagonal tiling, {6,6} and is an abstract type {6,6}. It is one of ten abstract regular polyhedra of index two with vertices on one orbit. Excavated dodecahedron In geometry, the excavated dodecahedron is a star polyhedron having 60 equilateral triangular faces. Its exterior surface represents the Efg stellation of the icosahedron. It appears in Magnus Wenninger's book
Dodecahedron of the wedge-shaped "roof" above the faces of the cube. When "h" = 1, the six cross-edges degenerate to points and a rhombic dodecahedron is formed. When "h" = 0, the cross-edges are absorbed in the facets of the cube, and the pyritohedron reduces to a cube. When "h" = , the multiplicative inverse of the golden ratio, the result is a regular dodecahedron. When "h" = , the conjugate of this value, the result is a regular great stellated dodecahedron. A reflected pyritohedron is made by swapping the nonzero coordinates above. The two pyritohedra can be superimposed to give