Prismatotruncated pentacontatetrapeton

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Prismatotruncated pentacontatetrapeton
Rank6
TypeUniform
Notation
Bowers style acronymPatom
Coxeter diagramx3o3x3o3x *c3x ()
Elements
Peta54 prismatotruncatodemipenteracts
72 cellirhombidodecatera
432 prismatorhombated pentachoric prisms
720 triangular duoprismatic prisms
Tera1440 triangular duoprisms
4320 triangular-square duoprisms
2160 square-hexagonal duoprisms
2160 truncated tetrahedral prisms
2160 cuboctahedral prisms
864 small rhombated pentachora
864 prismatorhombated pentachora
270 truncated hexadecachora
Cells4320+8640+8640 triangular prisms
2160 octahedra
6480+6480 cubes
4320 cuboctahedra
4320 truncated tetrahedra
8640 hexagonal prisms
Faces8640+17280 triangles, 12960+12960+25920 squares, 8640 hexagons
Edges25920+25920+6480
Vertices12960
Vertex figureIrregular bidiminished-rectified-pentachoric pyramid
Measures (edge length 1)
Circumradius
Hypervolume
Central density1
Number of external pieces1278
Related polytopes
ArmyPatom
RegimentPatom
ConjugateNone
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryE6×2, order 103680
ConvexYes
NatureTame

The prismatotruncated pentacontatetrapeton or patom, also called the runcitruncated 122 polytope, is a convex uniform polypeton. It consists of 54 prismatotruncated demipenteracts, 72 cellirhombidodecatera, 432 prismatorhombated pentachoric prisms, and 720 triangular duoprismatic prisms. 2 prismatotruncated demipenteracts, 1 cellirhombidodecateron, 4 prismatorhombated pentachoric prisms, and 1 triangular duoprismatic prism join at each vertex.

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