Difference between revisions 449123103 and 449123171 on enwiki

{{Uniform polyhedra db|Uniform polyhedron stat table|Scrid}}
In geometry, the '''small complex rhombicosidodecahedron''' (also known as the '''small complex ditrigonal rhombicosidodecahedron''') is a degenerate [[uniform star polyhedron]]. It has 62 faces (20 [[triangle]]s, 12 [[pentagram]]s and 30 [[square]]s), 120 (doubled) edges and 20 vertices. All edges are doubled (making it degenerate), sharing 4 faces, but are considered as two overlapping (contracted; show full)mbidodecadodecahedron''' (a compound of the [[ditrigonal dodecadodecahedron]] and the compound of five cubes) with vertex figure (5/3.4.5.4)/3 and the '''great complex rhombicosidodecahedron''' (a compound of the [[great ditrigonal dodecadodecahedron]] and the compound of five cubes) with vertex figure (5/4.4.3/2.4)/3. All three degenerate uniform polyhedra have each vertex really being three coincident vertices and each edge really being two coincident edges.


Their Coxeter-Dynkin diagrams are:

*Small complex rhombicosidodecahedron - {{CDD|node_1|5/2|node|3|node_1}}
*Complex rhombidodecadodecahedron - {{CDD|node_1|5/3|node|5|node_1}}
*Great complex rhombicosidodecahedron - {{CDD|node_1|5/4|node|3/2|node_1}}⏎
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They can all be constructed by cantellating regular polyhedra.
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==See also==
*[[Small complex icosidodecahedron]]
*[[Great complex icosidodecahedron]]
*[[Complex rhombidodecadodecahedron]]
*[[Great complex rhombicosidodecahedron]]

==References==
* {{KlitzingPolytopes|polyhedra-neu.htm|3D uniform polyhedra|sicdatrid}}
* {{KlitzingPolytopes|polyhedra-neu.htm|3D uniform polyhedra|cadditradid}}
* {{KlitzingPolytopes|polyhedra-neu.htm|3D uniform polyhedra|gicdatrid}}
{{geometry-stub}}
[[Category:Polyhedra]]