Excavated dodecahedron 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 "Polyhedron Models" as model 28, the "third stellation of icosahedron". It has the same external form as a certain facetting of the dodecahedron having 20 self-intersecting hexagons as faces. The non-convex hexagon face can be broken up into four equilateral triangles, three of which are the same size. A true excavated dodecahedron has the three congruent equilateral triangles as true faces of the polyhedron, while the interior equilateral
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,