Small omnicircumfacetopental trishecatonicosachoron

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Small omnicircumfacetopental trishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymSom fapathi
Elements
Cells120 icosahedra, 120 icosidodecahedra, 120 small rhombicosidodecahedra
Faces1200+2400 triangles, 1800 squares, 1440 pentagons
Edges3600
Vertices720
Edge figureid.srid.srid.ike.srid.srid.id
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesId–3–id: 120°
 Ike–3–srid: 120°
 Srid–4–srid: 90°
 Id–5–srid: 36°
Number of external pieces19320
Level of complexity33
Related polytopes
ArmyRox
RegimentRox
ConjugateGreat invertipental trishecatonicosachoron
Convex coreHecatonicosachoron
Abstract & topological properties
Flag count100800
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureWild

The small omnicircumfacetopental trishecatonicosachoron, or som fapathi, is a nonconvex uniform polychoron that consists of 120 icosahedra, 120 icosidodecahedra, and 120 small rhombicosidodecahedra. 2 icosahedra, 5 icosidodecahedra, and 10 small rhombicosidodecahedra join at eachv ertex.


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 rectified hexacosichoron.

External links[edit | edit source]