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 rhombihexahedron vertices, and 48 edges. It has 12 outer vertices which have the same vertex arrangement as the cuboctahedron, and 6 inner vertices with the vertex arrangement of an octahedron. As a surface geometry, it can be seen as visually similar to a Catalan solid, the disdyakis dodecahedron, with much taller rhombus-based pyramids joined to each face of a rhombic dodecahedron. Great rhombihexahedron In geometry, the great rhombihexahedron is a nonconvex uniform polyhedron, indexed as U. Its dual is the great rhombihexacron. Its vertex figure is a crossed quadrilateral. There is some controversy on how to colour the faces of this