Difference between revisions 471670918 and 490738328 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 (geometry)|square]]s), 120 (doubled) edges and 20 vertices. All edges are doubled (making it degenerate), sharing 4 faces, but are considered as two overlapping edges as a topological polyhedron.

It can be constructed from the vertex figure 3(<sup>5</sup>/<sub>2</sub>.4.3.4)<sup>3</sup>, thus making it look identical to thealso a [[cantellation (geometry)|cantellated]] [[great icosahedron]]. The "3" in front of this vertex figure indicates that each vertex in this degenerate polyhedron is in fact three [[coincidence (geometry)|coincident]] vertices.

==As a compound==
It can be seen as a [[polyhedron compound|compound]] of the [[small ditrigonal icosidodecahedron]], U<sub>30</sub>, and the [[compound of five cubes]]. It is also a [[facetting]] of the dodecahedron.

{| class=wikitable width=300
|+ '''Compound polyhedron'''
|[[File:Small ditrigonal icosidodecahedron.png|100px]]
(contracted; show full)yhedra are also facettings of the dodecahedron. They are the '''complex rhombidodecadodecahedron''' (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 icosidodecahedron]] and the compound of five cubes) with vertex figure (5/4.4.3/2.4)/3. All three degenerate uniform polyhedra have each vertex 
reallyin fact being three coincident vertices and each edge reallyin fact being two coincident edges.

They can all be constructed by [[cantellation (geometry)|cantellating]] regular polyhedra.

==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}}

[[Category:Polyhedra]]

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