Hecatonicosihexacosiquasitruncated prismatohecatonicosihexacosichoron

From Polytope Wiki
Jump to navigation Jump to search
Hecatonicosihexacosiquasitruncated prismatohecatonicosihexacosichoron
Rank4
TypeUniform
Notation
Bowers style acronymHixquitphix
Coxeter diagramx3x3x5x5/3*b ()
Elements
Cells720 decagonal prisms, 600 truncated octahedra, 120 great quasitruncated icosidodecahedra, 120 icosidodecatruncated icosidodecahedra
Faces3600+3600 squares, 2400+2400 hexagons, 1440 decagons, 1440 decagrams
Edges7200+7200+7200+7200
Vertices14400
Vertex figureIrregular tetrahedron, edge lengths 2 (2), 3 (2), (5+5)/2 (1), and (5–5)/2 (1)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesToe–6–gaquatid:
 Idtid–10–dip: 126°
 Gaquatid–4–dip:
 Idtid–10/3–gaquatid: 108°
 Toe–4–dip:
 Idtid–6–toe:
Number of external pieces717960
Level of complexity1883
Related polytopes
ArmySemi-uniform Gidpixhi, edge lengths (sides of hexagonal prisms), (remaining edges of dipentagons), (bases of hexagonal prisms)
RegimentHixquitphix
ConjugateHecatonicosihexacositruncated prismatohecatonicosihexacosichoron
Convex coreHecatonicosachoron
Abstract & topological properties
Flag count345600
Euler characteristic–1080
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The hecatonicosihexacosiquasitruncated prismatohecatonicosihexacosichoron, or hixquitphix, is a nonconvex uniform polychoron that consists of 720 decagonal prisms, 600 truncated octahedra, 120 great quasitruncated icosidodecahedra, and 120 icosidodecatruncated icosidodecahedra. 1 of each type of cell join at each vertex.

Cross-sections[edit | edit source]

Vertex coordinates[edit | edit source]

Vertex coordinates for a hecatonicosihexacosiquasitruncated prismatohecatonicosihexacosichoron of edge length 1 are given by all permutations of:

plus all even permutations of:

External links[edit | edit source]