Small hecatonicosafaceted hexacosidishecatonicosachoron

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Small hecatonicosafaceted hexacosidishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymShi fixady
Elements
Cells600 tetrahedra, 120 truncated great icosahedra, 120 small icosicosidodecahedra
Faces2400 triangles, 1440 pentagrams, 2400 hexagons
Edges3600+3600
Vertices2400
Vertex figureTriangular hemiantipodium, edge lengths 1 (top triangle), (5–1)/2 (base pseudo-triangle), and 3 (sides)
Measures (edge length 1)
Circumradius
Dichoral anglesSiid–6–tiggy: 120°
 Siid–3–tet:
 Siid–5/2–tiggy: 72°
Number of external pieces299040
Level of complexity955
Related polytopes
ArmySemi-uniform Sidpixhi
RegimentSadixady
ConjugateGreat hecatonicosafaceted hexacosidishecatonicosachoron
Abstract & topological properties
Euler characteristic600
OrientableNo
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The small hecatonicosafaceted hexacosidishecatonicosachoron, or shi fixady, is a nonconvex uniform polychoron that consists of 600 tetrahedra, 120 truncated great icosahedra, and 120 small icosicosidodecahedra. One tetrahedron, three truncated great icosahedra, and three small icosicosidodecahedra join at each vertex.

It also has 120 great stellated dodecahedra and 600 truncated tetrahedra 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 dishexacosidishecatonicosachoron.

External links[edit | edit source]