Great prismatotetracontoctachoric prism
Great prismatotetracontoctachoric prism | |
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File:Great prismatotetracontoctachoric prism.png | |
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Gippiccup |
Coxeter diagram | x x3x4x3x |
Elements | |
Tera | 192 square-hexagonal duoprisms, 48 great rhombicuboctahedral prisms, 2 great prismatotetracontoctachora |
Cells | 288+576 cubes, 384+384 hexagonal prisms, 144 octagonal prisms, 96 great rhombicuboctahedra |
Faces | 576+1152+1152+1152 squares, 768 hexagons, 288 octagons |
Edges | 1152+2304+2304 |
Vertices | 2304 |
Vertex figure | Phyllic disphenoidal pyramid, edge lengths √2, √3, √2+√2 (base), √2 (legs) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Shiddip–cube–shiddip: |
Gircope–hip–shiddip: 150° | |
Gircope–cube–shiddip: | |
Gircope–op–gircope: 135° | |
Gippic–girco–gircope: 90° | |
Gircope–hip–shiddip: 90° | |
Height | 1 |
Central density | 1 |
Number of external pieces | 242 |
Level of complexity | 60 |
Related polytopes | |
Army | Gippiccup |
Regiment | Gippiccup |
Dual | Disphenoidal chilliahecatonicpentacontadichoric tegum |
Conjugate | Great quasiprismatotetracontoctachoric prism |
Abstract & topological properties | |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | F4×2×A1, order 4608 |
Convex | Yes |
Nature | Tame |
The great prismatotetracontoctachoric prism or gippiccup is a prismatic uniform polyteron that consists of 2 great prismatotetracontoctachora, 48 great rhombicuboctahedral prisms, and 192 square-hexagonal duoprisms. 1 great prismatotetracontoctachoron, 2 great rhombicuboctahedral prisms, and 2 square-hexagonal duoprisms join at each vertex. As the name suggests, it is a prism based on the great prismatotetracontoctachoron, which also makes it a convex segmentoteron.
This polyteron can be alternated into a snub tetracontoctachoric antiprism, although it cannot be made uniform, or it can be subsymmetrically faceted into a runcicantic snub icositetrachoric alterprism, although it cannot be made scaliform.
Vertex coordinates[edit | edit source]
The vertices of a great prismatotetracontoctachoric prism of edge length 1 are given by all permutations and sign changes of the first four coordinates of:
External links[edit | edit source]
- Klitzing, Richard. "Gippiccup".