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
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