Great prismatotetracontoctachoric prism

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Great prismatotetracontoctachoric prism
File:Great prismatotetracontoctachoric prism.png
Rank5
TypeUniform
Notation
Bowers style acronymGippiccup
Coxeter diagramx x3x4x3x
Elements
Tera192 square-hexagonal duoprisms, 48 great rhombicuboctahedral prisms, 2 great prismatotetracontoctachora
Cells288+576 cubes, 384+384 hexagonal prisms, 144 octagonal prisms, 96 great rhombicuboctahedra
Faces576+1152+1152+1152 squares, 768 hexagons, 288 octagons
Edges1152+2304+2304
Vertices2304
Vertex figurePhyllic disphenoidal pyramid, edge lengths 2, 3, 2+2 (base), 2 (legs)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesShiddip–cube–shiddip:
 Gircope–hip–shiddip: 150°
 Gircope–cube–shiddip:
 Gircope–op–gircope: 135°
 Gippic–girco–gircope: 90°
 Gircope–hip–shiddip: 90°
Height1
Central density1
Number of external pieces242
Level of complexity60
Related polytopes
ArmyGippiccup
RegimentGippiccup
DualDisphenoidal chilliahecatonicpentacontadichoric tegum
ConjugateGreat quasiprismatotetracontoctachoric prism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryF4×2×A1, order 4608
ConvexYes
NatureTame

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]