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Truncated dodecadodecahedron
Polyhedron with 54 faces / From Wikipedia, the free encyclopedia
In geometry, the truncated dodecadodecahedron (or stellatruncated dodecadodecahedron) is a nonconvex uniform polyhedron, indexed as U59. It is given a Schläfli symbol t0,1,2{5⁄3,5}. It has 54 faces (30 squares, 12 decagons, and 12 decagrams), 180 edges, and 120 vertices.[1] The central region of the polyhedron is connected to the exterior via 20 small triangular holes.
Truncated dodecadodecahedron | |
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Type | Uniform star polyhedron |
Elements | F = 54, E = 180 V = 120 (χ = −6) |
Faces by sides | 30{4}+12{10}+12{10/3} |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Wythoff symbol | 2 5 5/3 | |
Symmetry group | Ih, [5,3], *532 |
Index references | U59, C75, W98 |
Dual polyhedron | Medial disdyakis triacontahedron |
Vertex figure | ![]() 4.10/9.10/3 |
Bowers acronym | Quitdid |
![](http://upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Truncated_dodecadodecahedron.stl/640px-Truncated_dodecadodecahedron.stl.png)
The name truncated dodecadodecahedron is somewhat misleading: truncation of the dodecadodecahedron would produce rectangular faces rather than squares, and the pentagram faces of the dodecadodecahedron would turn into truncated pentagrams rather than decagrams. However, it is the quasitruncation of the dodecadodecahedron, as defined by Coxeter, Longuet-Higgins & Miller (1954).[2] For this reason, it is also known as the quasitruncated dodecadodecahedron.[3] Coxeter et al. credit its discovery to a paper published in 1881 by Austrian mathematician Johann Pitsch.[4]