- Ditrigonal dodecadodecahedron
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Ditrigonal dodecadodecahedron Type Uniform star polyhedron Elements F = 24, E = 60
V = 20 (χ = −16)Faces by sides 12{5}+12{5/2} Wythoff symbol 3 | 5/3 5 Symmetry group Ih, [5,3], *532 Index references U41, C53, W80
(5.5/3)3
(Vertex figure)
Medial triambic icosahedron
(dual polyhedron)In geometry, the Ditrigonal dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U41.
Contents
Related polyhedra
Its convex hull is a regular dodecahedron. It additionally shares its edge arrangement with the small ditrigonal icosidodecahedron (having the pentagrammic faces in common), the great ditrigonal icosidodecahedron (having the pentagonal faces in common), and the regular compound of five cubes.
Small ditrigonal icosidodecahedron
Great ditrigonal icosidodecahedron
Ditrigonal dodecadodecahedron
Dodecahedron (convex hull)
Compound of five cubesFurthermore, 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 the hyperbolic order-6 pentagonal tiling, by distorting the pentagrams back into regular pentagons. As such, it is a regular polyhedron of index two:[1]
See also
References
- ^ The Regular Polyhedra (of index two), David A. Richter
External links
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