Small rhombated small stellated hecatonicosachoron |
---|
|
Rank | 4 |
---|
Type | Uniform |
---|
Notation |
---|
Bowers style acronym | Sirsashi |
---|
Coxeter diagram | x5/2o5x3o () |
---|
Elements |
---|
Cells | 1200 triangular prisms, 120 icosidodecahedra, 120 rhombidodecadodecahedra |
---|
Faces | 2400 triangles, 3600 squares, 1440 pentagons, 720 pentagrams |
---|
Edges | 3600+7200 |
---|
Vertices | 3600 |
---|
Vertex figure | Wedge, edge lengths (1+√5)/2 (two edges of base rectangle), 1 (other 2 base edges), √2 (side edges), and (√5–1)/2 (top edge) |
---|
Measures (edge length 1) |
---|
Circumradius | |
---|
Hypervolume | |
---|
Dichoral angles | Raded–4–trip: |
---|
| Id–3–trip: 150° |
---|
| Raded–5–id: 144° |
---|
| Raded–5/2–raded: 144° |
---|
Related polytopes |
---|
Army | Semi-uniform Xhi, edge lengths (pentagons), (triangles) |
---|
Regiment | Sirsashi |
---|
Conjugate | Small rhombated great grand hecatonicosachoron |
---|
Abstract & topological properties |
---|
Flag count | 129600 |
---|
Euler characteristic | –480 |
---|
Orientable | Yes |
---|
Properties |
---|
Symmetry | H4, order 14400 |
---|
Convex | No |
---|
Nature | Tame |
---|
The small rhombated small stellated hecatonicosachoron, or sirsashi, is a nonconvex uniform polychoron that consists of 1200 triangular prisms, 120 icosidodecahedra, and 120 rhombidodecadodecahedra. 1 icosidodecahedron, 2 triangular prisms, and 2 rhombidodecadodecahedra join at each vertex. it can be obtained by cantellating the small stellated hecatonicosachoron.
Coordinates for the vertices of a small rhombated small stellated hecatonicosachoron of edge length 1 are given by all permutations of:
- ,
- ,
- ,
- ,
- ,
together with all even permutations of:
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- .
The small rhombated small stellated hecatonicosachoron is the colonel of a regiment of 7 members. Its other members include the medial retrosphenoverted hecatonicosihexacosihecatonicosachoron, rhombic small hecatonicosihexacosichoron, pseudorhombic small hexacosihecatonicosachoron, grand rhombic small dishecatonicosachoron, small hexacosihecatonicosintercepted dishecatonicosachoron, and small hecatonicosintercepted prismatodishecatonicosachoron.
truncations |
---|
Name | OBSA | Schläfli symbol | CD diagram | Image |
---|
Small stellated hecatonicosachoron | sishi | {5/2,5,3} | | |
---|
Rectified small stellated hecatonicosachoron | rasishi | r{5/2,5,3} | | |
---|
Rectified faceted hexacosichoron | rofix | r{3,5,5/2} | | |
---|
Faceted hexacosichoron | fix | {3,5,5/2} | | |
---|
(degenerate, quadruple cover of hi) | | t{5/2,5,3} | | |
---|
Small rhombated small stellated hecatonicosachoron | sirsashi | rr{5/2,5,3} | | |
---|
Prismatodishecatonicosachoron | padohi | t0,3{5/2,5,3} | | |
---|
Small hecatonicosihecatonicosachoron | shihi | 2t{5/2,5,3} | | |
---|
Small rhombated faceted hexacosichoron | sirfix | rr{3,5,5/2} | | |
---|
Truncated faceted hexacosichoron | tiffix | t{3,5,5/2} | | |
---|
(degenerate, sirdhi + 720(10/2)) | | t0,1,2{5/2,5,3} | | |
---|
(degenerate, six fipady + 720 double covers of pip) | | t0,1,3{5/2,5,3} | | |
---|
Prismatorhombated stellated hecatonicosachoron | pirshi | t0,2,3{5/2,5,3} | | |
---|
Great rhombated faceted hexacosichoron | girfix | t1,2,3{5/2,5,3} | | |
---|
(degenerate, sripady + 720 double covers of pip) | | t0,1,2,3{5/2,5,3} | | |
---|