Great quasidisprismatotesseractihexadecachoron

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Great quasidisprismatotesseractihexadecachoron
Rank4
TypeUniform
Notation
Bowers style acronymGaquidpoth
Coxeter diagramx4/3x3x3x ()
Elements
Cells32 hexagonal prisms, 24 octagrammic prisms, 16 truncated octahedra, 8 quasitruncated cuboctahedra
Faces96+96+96 squares, 64+64 hexagons, 48 octagrams
Edges192+192+192+192
Vertices384
Vertex figureIrregular tetrahedron, edge lengths 2 (3), 3 (2), and 2–2 (1)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesStop–4–hip:
 Quitco–8/3–stop: 135°
 Quitco–4–hip:
 Quitco–6–toe: 60°
 Toe–4–stop: 45°
 Toe–6–hip: 30°
Number of external pieces536
Level of complexity104
Related polytopes
ArmySemi-uniform Gidpith, edge lengths (octagons), (remaining edges of great rhombicuboctahedra), 1 (sides of octagonal prisms)
RegimentGaquidpoth
ConjugateGreat disprismatotesseractihexadecachoron
Convex coreSemi-uniform truncated hexadecachoron
Abstract & topological properties
Flag count9216
Euler characteristic0
OrientableYes
Properties
SymmetryB4, order 384
ConvexNo
NatureTame

The great quasidisprismatotesseractihexadecachoron, or gaquidpoth, is a nonconvex uniform polychoron that consists of 32 hexagonal prisms, 24 octagrammic prisms, 16 truncated octahedra, and 8 quasitruncated cuboctahedra. 1 of each type of cell join at each vertex.

The great quasidisprismatotesseractihexadecachoron can be vertex-inscribed into a great prismatotrisicositetrachoron.

Cross-sections[edit | edit source]

Vertex coordinates[edit | edit source]

Vertex coordinates for a great quasidisprismatotesseractihexadecachoron of edge length 1 are given by all permutations of:

External links[edit | edit source]