Ditrigonal dodecadodecahedron
In geometry, the ditrigonal dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U41. It has 24 faces, 60 edges, and 20 vertices. It has extended Schläfli symbol b, as a blended great dodecahedron, and Coxeter diagram. It has 4 Schwarz triangle equivalent constructions, for example Wythoff symbol 3 | 5, and Coxeter diagram.
Related polyhedra
Its convex hull is a regular dodecahedron. It additionally shares its edge arrangement with the small ditrigonal icosidodecahedron, the great ditrigonal icosidodecahedron, and the regular compound of five cubes.| a | a | b |
| = | = | = |
Small ditrigonal icosidodecahedron | Great ditrigonal icosidodecahedron | Ditrigonal dodecadodecahedron |
Dodecahedron | Compound of five cubes | - |
Furthermore, it may be viewed as a facetted dodecahedron: the pentagonal faces may be inscribed within the dodecahedron's pentagons. Its dual, the medial triambic icosahedron, is a stellation of the icosahedron.
It is topologically equivalent to a quotient space of the hyperbolic order-6 pentagonal tiling, by distorting the pentagrams back into regular pentagons. As such, it is a regular polyhedron of index two: