Small prismatohecatonicosintercepted dishecatonicosachoron
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Small prismatohecatonicosintercepted dishecatonicosachoron | |
---|---|
Rank | 4 |
Type | Uniform |
Notation | |
Bowers style acronym | Sophinady |
Elements | |
Cells | 720 pentagonal prisms, 120 icosidodecahedra, 120 great dodecicosidodecahedra, 120 quasitruncated dodecahedra |
Faces | 2400 triangles, 3600 squares, 1440 pentagons, 720 pentagrams, 720 decagons, 1440 decagrams |
Edges | 3600+7200 |
Vertices | 3600 |
Vertex figure | Inverted wedge, edge lengths 1 (2), Template:Radi (4), (1+√5)/2 (2), (√5–1)/2 (1), √(5+√5)/2 (2), and √(5–√5)/2 (4) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dichoral angles | Gaddid–5/2–gaddid: 144° |
Gaddid–10/3–quitdid: 72° | |
Gaddid–3–id: 60° | |
Quitdid–4–pip: | |
Id–5–pi: 54° | |
Quitdid–10–quitdid: 36° | |
Related polytopes | |
Army | Semi-uniform srix |
Regiment | Wavathi |
Conjugate | Hecatonicosintercepted hecatonicosiprismatohecatonicosachoron |
Abstract & topological properties | |
Euler characteristic | 2040 |
Orientable | Yes |
Properties | |
Symmetry | H4, order 14400 |
Convex | No |
Nature | Wild |
The small prismatohecatonicosintercepted dishecatonicosachoron, or sophinady, is a nonconvex uniform polychoron that consists of 120 icosidodecahedra, 120 great dodecicosidodecahedra, 720 pentagonal prisms, and 120 quasitruncated dodecadodecahedra. One icosidodecahedron, two great dodecicosidodecahedra, two pentagonal prisms, and four quasitruncated dodecadodecahedra join at each vertex.
Vertex coordinates[edit | edit source]
The vertices are the same as those of the regiment colonel, the sphenoverted trishecatonicosachoron.
External links[edit | edit source]
- Bowers, Jonathan. "Category 6: Sphenoverts" (#282).