Prismatodishecatonicosachoron
Prismatodishecatonicosachoron | |
---|---|
Rank | 4 |
Type | Uniform |
Notation | |
Bowers style acronym | Padohi |
Coxeter diagram | x5/2o5o3x () |
Elements | |
Cells | 1200 triangular prisms, 720 pentagrammic prisms, 120 icosahedra, 120 small stellated dodecahedra |
Faces | 2400 triangles, 3600 squares, 1440 pentagrams |
Edges | 3600+3600 |
Vertices | 1440 |
Vertex figure | Pentagonal antipodium, edge lengths 1 (large base), (√5–1)/2 (small base), and √2 (sides) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dichoral angles | Stip–4–trip: |
Sissid–5/2–stip: 162° | |
Ike–3–trip: 150° | |
Central density | 4 |
Number of external pieces | 22080 |
Related polytopes | |
Army | Semi-uniform Tex, edge lengths (icosahedra), (surrounded by truncated tetrahedra) |
Regiment | Padohi |
Conjugate | Quasiprismatodishecatonicosachoron |
Abstract & topological properties | |
Flag count | 115200 |
Euler characteristic | –480 |
Orientable | Yes |
Properties | |
Symmetry | H_{4}, order 14400 |
Convex | No |
Nature | Tame |
The prismatodishecatonicosachoron, or padohi, is a nonconvex uniform polychoron that consists of 120 icosahedra, 120 small stellated dodecahedra, 1200 triangular prisms, and 720 pentagrammic prisms. 1 icosahedron, 1 small stellated dodecahedron, 5 triangular prisms, and 5 pentagrammic prisms join at each vertex. It is the result of expanding the cells of either a small stellated hecatonicosachoron or a faceted hexacosichoron outwards.
The prismatodishecatonicosachoron contains the vertices of a prismatorhombisnub icositetrachoron.
Blending 10 prismatodishecatonicosachora results in the small difusiprismatosnub diprismatosnub disdishexacosichoron, which is scaliform.
Vertex coordinates[edit | edit source]
The vertices of a prismatodishecatonicosachoron of edge length 1 are given by all permutations of:
plus all even permutations of:
Related polychora[edit | edit source]
The prismatodishecatonicosachoron is the colonel of a regiment that includes 81 uniform members, as well as 78 fissary uniforms, 18 normal and 59 fissary scaliforms, and 1 scaliform compound.
Name | OBSA | CD diagram | Picture |
---|---|---|---|
Small stellated hecatonicosachoron | sishi | x5/2o5o3o () | |
(degenerate, quadruple cover of hi) | x5/2x5o3o () | ||
Rectified small stellated hecatonicosachoron | rasishi | o5/2x5o3o () | |
Small hecatonicosihecatonicosachoron | shihi | o5/2x5x3o () | |
Rectified faceted hexacosichoron | rofix | o5/2o5x3o () | |
Truncated faceted hexacosichoron | tiffix | o5/2o5x3x () | |
Faceted hexacosichoron | fix | o5/2o5o3x () | |
Small rhombated small stellated hecatonicosachoron | sirsashi | x5/2o5x3o () | |
(degenerate, sirdhi + 720(10/2)) | x5/2x5x3o () | ||
Small rhombated faceted hexacosichoron | sirfix | o5/2x5o3x () | |
Great rhombated faceted hexacosichoron | girfix | o5/2x5x3x () | |
Prismatodishecatonicosachoron | padohi | x5/2o5o3x () | |
(degenerate, six fipady + 720 double covers of pip) | x5/2x5o3x () | ||
Prismatorhombated stellated hecatonicosachoron | pirshi | x5/2o5x3x () | |
(degenerate, sripady + 720 double covers of pip) | x5/2x5x3x () |
External links[edit | edit source]
- Bowers, Jonathan. "Category 21: Padohi Regiment" (#985).
- Bowers, Jonathan. "How to Make Padohi".
- Klitzing, Richard. "padohi".