Grand antiprism
Uniform 4-polytope bounded by 320 cells / From Wikipedia, the free encyclopedia
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In geometry, the grand antiprism or pentagonal double antiprismoid is a uniform 4-polytope (4-dimensional uniform polytope) bounded by 320 cells: 20 pentagonal antiprisms, and 300 tetrahedra. It is an anomalous, non-Wythoffian uniform 4-polytope, discovered in 1965 by Conway and Guy.[1][2] Topologically, under its highest symmetry, the pentagonal antiprisms have D5d symmetry and there are two types of tetrahedra, one with S4 symmetry and one with Cs symmetry.
Grand antiprism | |
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(Schlegel diagram wireframe) | |
Type | Uniform 4-polytope |
Uniform index | 47 |
Cells | 100+200 (3.3.3) 20 (3.3.3.5) |
Faces | 20 {5} 700 {3} |
Edges | 500 |
Vertices | 100 |
Vertex figure | Sphenocorona |
Symmetry group | Ionic diminished Coxeter group [[10,2+,10]] of order 400 |
Properties | convex |
A net showing two disjoint rings of 10 antiprisms. 200 tetrahedra (yellow) are in face contact with the antiprisms and 100 tetrahedra (red) contact only other tetrahedra. |