Stericantitruncated 5-simplex

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Stericantitruncated 5-simplex
Rank5
TypeUniform
Notation
Bowers style acronymCograx
Coxeter diagramx3x3x3o3x ()
Elements
Tera20 triangular-hexagonal duoprisms, 15 cuboctahedral prisms, 15 truncated octahedral prisms, 6 great rhombated pentachora, 6 prismatorhombated pentachora
Cells60+60+60 triangular prisms, 90 cubes, 60+60 hexagonal prisms, 30 truncated tetrahedra, 30 cuboctahedra, 30 truncated octahedra
Faces120+120 triangles, 180+180+180+180 squares, 60+120 hexagons
Edges180+180+360+360
Vertices360
Vertex figureSkew rectangular pyramidal pyramid, base edge lengths 1 and 2, remaining edge lengths 2 (6) and 3 (3)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesTope–hip–thiddip: 135°
 Cope–trip–thiddip: 135°
 Prip–co–cope:
 Grip–toe–tope:
 Cope–cube–tope: 120°
 Prip–trip–thiddip:
 Grip–trip–cope:
 Prip–hip–tope:
 Prip–tut–grip:
Central density1
Number of external pieces62
Level of complexity80
Related polytopes
ArmyCograx
RegimentCograx
DualDeltopyramidal pyramidal triacosihexecontateron
ConjugateNone
Abstract & topological properties
Flag count57600
Euler characteristic2
OrientableYes
Properties
SymmetryA5, order 720
ConvexYes
NatureTame

The stericantitruncated 5-simplex, also called the celligreatorhombated hexateron or cograx, is a convex uniform 5-polytope. It consists of 20 triangular-hexagonal duoprisms, 15 cuboctahedral prisms, 15 truncated octahedral prisms, 6 great rhombated pentachora, and 6 prismatorhombated pentachora. 1 prismatorhombated pentachoron, 1 cuboctahedral prism, 1 great rhombated pentachoron, 1 triangular-hexagonal duoprism, and 2 truncated octahedral prisms join at each vertex. As the name suggests, it is the stericantitruncation of the 5-simplex.

Vertex coordinates[edit | edit source]

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

  • .

Gallery[edit | edit source]

Related polytopes[edit | edit source]

The stericantitruncated 5-simplex is the colonel of a three-member regiment that also includes the retrocelligreatorhombated hexateron and lepidocelligreatorhombated hexateron.

External links[edit | edit source]