Small hecatonicosafaceted prismatohecatonicosihexacosichoron

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Small hecatonicosafaceted prismatohecatonicosihexacosichoron
Rank4
TypeUniform
Notation
Bowers style acronymShif phix
Elements
Cells600 tetrahedra, 720 pentagonal prisms, 120 small rhombicosidodecahedra
Faces2400 triangles, 3600 squares, 1440 pentagons
Edges3600+3600
Vertices2400
Vertex figureIrregular triangular hemiantipodium, edge lengths 1 (top triangle), (1+5)/2 (base pseudo-triangle), and 2 (sides)
Measures (edge length 1)
Circumradius
Dichoral anglesSrid–4–pip:
 Srid–3–tet:
 Srid–5–pip: 18°
Number of external pieces8880
Level of complexity24
Related polytopes
ArmySidpixhi
RegimentSidpixhi
ConjugateGreat hecatonicosafaceted prismatohecatonicosihexacosichoron
Abstract & topological properties
Flag count115200
Euler characteristic1200
OrientableNo
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The small hecatonicosafaceted prismatohecatonicosihexacosichoron, or shif phix, is a nonconvex uniform polychoron that consists of 600 tetrahedra, 720 pentagonal prisms, and 120 small rhombicosidodecahedra. One tetrahedron, three pentagonal prisms, and three small rhombicosidodecahedra join at each vertex.

It also has 120 dodecahedra and 1200 triangular prisms as pseudofacets.

Gallery[edit | edit source]

Card with cell counts, vertex figure, and cross-sections.


Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the small disprismatohexacosihecatonicosachoron.

External links[edit | edit source]