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Small complex icosidodecahedron
Type
Uniform star polyhedron
Elements
F = 32, E = 60 (30x2) V = 12 (χ = −16)
Faces by sides
20{3}+12{5}
Coxeter diagram
Wythoff symbol
5 | 3/2 5
Symmetry group
Ih, [5,3], *532
Index references
U-, C-, W-
Dual polyhedron
Small complex icosidodecacron
Vertex figure
(3/2.5)5 (3.5)5/3
Bowers acronym
Cid
In geometry, the small complex icosidodecahedron is a degenerate uniform star polyhedron. Its edges are doubled, making it degenerate. The star has 32 faces (20 triangles and 12 pentagons), 60 (doubled) edges and 12 vertices and 4 sharing faces. The faces in it are considered as two overlapping edges as topological polyhedron.
A small complex icosidodecahedron can be constructed from a number of different vertex figures.
A very similar figure emerges as a geometrical truncation of the great stellated dodecahedron, where the pentagram faces become doubly-wound pentagons ({5/2} --> {10/2}), making the internal pentagonal planes, and the three meeting at each vertex become triangles, making the external triangular planes.
and 20 Related for: Small complex icosidodecahedron information
In geometry, the smallcomplexicosidodecahedron is a degenerate uniform star polyhedron. Its edges are doubled, making it degenerate. The star has 32...
In geometry, the great complexicosidodecahedron is a degenerate uniform star polyhedron. It has 12 vertices, and 60 (doubled) edges, and 32 faces, 12...
Rhombicosacron SmallcomplexicosidodecahedronSmall ditrigonal dodecacronic hexecontahedron Small dodecacronic hexecontahedron Small dodecahemicosacron Small dodecahemidodecacron...
the smallcomplexicosidodecahedron (compound of icosahedron and great dodecahedron) and the great complexicosidodecahedron (compound of small stellated...
include: Smallcomplexicosidodecahedron Great complexicosidodecahedronSmallcomplex rhombicosidodecahedron Great complex rhombicosidodecahedron Complex...
with the great icosahedron; the compound with both is the great complexicosidodecahedron. There are four related uniform polyhedra, constructed as degrees...
shares its edge arrangement with the small ditrigonal icosidodecahedron, the great ditrigonal icosidodecahedron, and the ditrigonal dodecadodecahedron...
degenerate polyhedron included in the above list, such as the smallcomplexicosidodecahedron. This interpretation of edges being coincident allows these...
Archimedean solid can contain, as with the truncated dodecahedron and icosidodecahedron. There are ten regular star polychora in the fourth dimension, all...
geometric polyhedra. But where a polyhedral name is given, such as icosidodecahedron, the most symmetrical geometry is almost always implied, unless otherwise...
Kepler–Poinsot polyhedra. A rectified regular dodecahedron forms an icosidodecahedron. The regular dodecahedron has icosahedral symmetry Ih, Coxeter group...
the squares yellow, and the triangles blue. In the picture of the smallcomplex rhombicosidodecahedron, the pentagons are red, the squares blue (hidden...
Wenninger's Polyhedron Models) An unknown number of stellations of the icosidodecahedron; there are 7071671 non-chiral stellations, but the number of chiral...
the infinite family of cuploids. It can be obtained as a slice of the smallcomplex rhombicosidodecahedron. As in all cupolae, the base polygon has twice...
tetrahedra, the compound of ten tetrahedra, rhombic triacontahedron, icosidodecahedron, truncated icosahedron, truncated dodecahedron, and rhombicosidodecahedron...
quasi-symmetry, T = 3 can be presented as a truncated dodecahedron, an icosidodecahedron, or a truncated icosahedron and their respective duals a triakis icosahedron...
icosahedron. ( 0 , − 30 s , − 30 s ) {\displaystyle (0,-30s,-30s)} for the icosidodecahedron. ( 0 , 30 s , 30 s ) {\displaystyle (0,30s,30s)} for the rhombicosidodecahedron...
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