Great prismatohexadecadisoctachoron

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Great prismatohexadecadisoctachoron
Rank4
TypeUniform
Notation
Bowers style acronymGiphado
Coxeter diagramx4/3x3x3/2o3*b()
Elements
Cells32 triangular prisms, 16 octahemioctahedra, 8 quasitruncated hexahedra, 8 quasitruncated cuboctahedra
Faces64+64 triangles, 96 squares, 64 hexagons, 48 octagrams
Edges96+192+192
Vertices192
Vertex figureSkewed bowtie pyramid, base edge lengths 1, 3, 1, 3; lateral edge lengths 2, 2, 2–2, 2–2
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesOho–6–quitco: 120°
 Quith–8/3–quitco: 90°
 Oho–3–quith: 60°
 Quitco–4–trip:
 Oho–3–trip: 30°
Related polytopes
ArmySemi-uniform Prit, edge lengths (small rhombicuboctahedra), (sides of square prisms)
RegimentQuiproh
ConjugateSmall prismatohexadecadisoctachoron
Abstract & topological properties
Flag count6144
Euler characteristic–16
OrientableYes
Properties
SymmetryB4, order 384
ConvexNo
NatureTame

The great prismatohexadecadisoctachoron, or giphado, is a nonconvex uniform polychoron that consists of 32 triangular prisms, 16 octahemioctahedra, 8 quasitruncated hexahedra, and 8 quasitruncated cuboctahedra. 1 triangular prism, 1 quasitruncated hexahedron, 1 octahemioctahedron, and 2 quasitruncated cuboctahedra join at each vertex.

3 copies of this polychoron can blend to form the great pseudorhombic disicositetrachoron, with the octahemioctahedron cells blending out.

Cross-sections[edit | edit source]

Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the quasiprismatorhombated hexadecachoron.

External links[edit | edit source]