Great prismatotetracontoctachoron

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Great prismatotetracontoctachoron
Rank4
TypeUniform
Notation
Bowers style acronymGippic
Coxeter diagramx3x4x3x ()
Elements
Cells192 hexagonal prisms, 48 great rhombicuboctahedra
Faces288+576 squares, 384 hexagons, 144 octagons
Edges1152+1152
Vertices1152
Vertex figurePhyllic disphenoid, edge lengths 2 (3), 3 (2), and 2+2 (1)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesHip–4–hip:
 Girco–6–hip: 150°
 Girco–4–hip:
 Girco–8–girco: 135°
Central density1
Number of external pieces240
Level of complexity12
Related polytopes
ArmyGippic
RegimentGippic
DualDisphenoidal chiliahecatonpentaconta-dichoron
ConjugateGreat quasiprismatotetracontocta-choron
Abstract & topological properties
Flag count27648
Euler characteristic0
OrientableYes
Properties
SymmetryF4×2, order 2304
ConvexYes
NatureTame

The great prismatotetracontoctachoron, or gippic, also commonly called the omnitruncated 24-cell, is a convex uniform polychoron that consists of 192 hexagonal prisms and 48 great rhombicuboctahedra. 2 hexagonal prisms and 2 great rhombicuboctahedra join at each vertex. It is the omnitruncate of the F4 family of uniform polychora.

This polychoron can be alternated into a snub tetracontoctachoron, although it cannot be made uniform.

Cross-sections[edit | edit source]

Vertex coordinates[edit | edit source]

The vertices of a great prismatotetracontoctachoron of edge length 1 are given by all permutations of:

  • ,
  • ,
  • .

Representations[edit | edit source]

A great prismatotetracontoctachoron has the following Coxeter diagrams:

  • x3x4x3x () (full symmetry)
  • xux4wxx3xxx3xwX&#zx (B4 symmetry)

Semi-uniform variant[edit | edit source]

The great prismatotetracontoctachoron has a semi-uniform variant of the form x3y4y3x that maintains its full symmetry. This variant uses 48 great rhombicuboctahedra of form y4y3x and 192 ditrigonal prisms of form x x3y as cells, with 2 edge lengths.

With edges of length a and b (so that it is represented by a3b4b3a), its circumradius is given by .

If it has only single icositetrachoric symmetry, the variant is called a great disprismatoicositetricositetrachoron.

External links[edit | edit source]