Omnitruncated 5-simplex

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Omnitruncated 5-simplex
Rank5
TypeUniform
Notation
Bowers style acronymGocad
Coxeter diagramx3x3x3x3x ()
Elements
Tera20 hexagonal duoprisms, 30 truncated octahedral prisms, 12 great prismatodecachora
Cells90 cubes, 120+120+120 hexagonal prisms, 30+60 truncated octahedra
Faces180+180+360+360 squares, 240+240 hexagons
Edges360+720+720
Vertices720
Vertex figurePhyllic disphenoidal pyramid, edge lengths 2 (6) and 3 (4)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesTope–hip–hiddip: 135°
 Gippid–toe–tope:
 Tope–cube–tope: 120°
 Gippid–hip–hiddip:
 Gippid–hip–tope:
 Gippid–toe–gippid:
Central density1
Number of external pieces62
Level of complexity60
Related polytopes
ArmyGocad
RegimentGocad
DualDisphenoidal pyramidal heptacosiicosateron
ConjugateNone
Abstract & topological properties
Flag count86400
Euler characteristic2
OrientableYes
Properties
SymmetryA5×2, order 1440
ConvexYes
NatureTame

The omnitruncated 5-simplex, also called the great cellated hexateron, great cellidodecateron, or gocad, is a convex uniform 5-polytope. It consists of 20 hexagonal duoprisms, 30 truncated octahedral prisms, and 12 great prismatodecachora. 2 great prismatodecachora, 2 truncated octahedral prisms, and 1 hexagonal duoprism join at each vertex. As the name suggests, it is the omnitruncate of the A5 family.

This polyteron can be alternated into a snub dodecateron, but that cannot be made uniform.

It is the 6th-order permutohedron, and therefore fills 5D space.

Vertex coordinates[edit | edit source]

The vertices of a omnitruncated 5-simplex of edge length 1 can be given in 6 dimensions as all permutations of:

  • .

Gallery[edit | edit source]

External links[edit | edit source]