Chamfered dodecahedron The chamfered dodecahedron is a convex polyhedron with 80 vertices, 120 edges, and 42 faces: 30 hexagons and 12 pentagons. It is constructed as a chamfer (geometry) (edge-truncation) of a regular dodecahedron. The pentagons are reduced in size and new hexagonal faces are added in place of all the original edges. Its dual is the pentakis icosidodecahedron. It is also called a truncated rhombic triacontahedron, constructed as a truncation of the rhombic triacontahedron. It can more accurately be called In geometry, chamfering or edge-truncation is a Conway polyhedron notation operation that modifies one polyhedron into another. It is similar to expansion, moving faces apart and outward, but also maintain the original vertices. For polyhedra, this operation adds a new hexagonal face in place of each original edge. A polyhedron with e edges will have a chamfered form containing 2e new vertices, 3e new edges, and e new hexagonal faces. The chamfered cube is the Minkowski sum of a rhombic dodecahedron and a cube of side length 1 when eight vertices of the rhombic dodecahedron are at. ( ± 1 , ± 1 , ± 1 ) {\displaystyle (\pm 1,\pm 1,\pm 1)}. and its six vertices are at the permutations of. The truncated icosahedron looks similar, but its hexagons correspond to the 20 vertices of the dodecahedron, rather than to its 30 edges. Category:Chamfered dodecahedron. From Wikimedia Commons, the free media repository. Jump to navigation Jump to search. chamfered dodecahedron or truncated rhombic triacontahedron. Media in category "Chamfered dodecahedron". The following 4 files are in this category, out of 4 total. 29. Chamfered dodecahedron ⓠThe chamfered dodecahedron is a convex polyhedron with 80 vertices,120 edges, and 42 faces,30 hexagons and 12 pentagons. It is constructed as a chamfer of a regular dodecahedron, the pentagons are reduced in size and new hexagonal faces are added in place of all the original edges. Its dual is the pentakis icosidodecahedron and it is also called a truncated rhombic triacontahedron, constructed as a truncation of the rhombic triacontahedron. The tetrated dodecahedron is a near-miss Johnson solid. It was first discovered in 2002 by Alex Doskey. It was then independently rediscovered in 2003 and named by Robert Austin. It has 28 faces: twelve regular pentagons arranged in four panels of three pentagons each, four equilateral triangles (shown in blue), and six pairs of isosceles triangles (shown in yellow). All edges of the tetrated dodecahedron have the same length, except for the shared bases of these isosceles triangles, which are.