Cantitruncated 5-simplex

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Cantitruncated 5-simplex
Rank5
TypeUniform
Notation
Bowers style acronymGarx
Coxeter diagramx3x3x3o3o ()
Elements
Tera15 tetrahedral prisms, 6 truncated pentachora, 6 great rhombated pentachora
Cells30 tetrahedra, 60 triangular prisms, 30 truncated tetrahedra, 15 truncated octahedra
Faces120 triangles, 90 squares, 20+60 hexagons
Edges60+60+180
Vertices120
Vertex figureTriangular pyramidal pyramid, edge lengths 1 (base), 2 (sides of pyramid 1), and 3 (sides of pyramid 2 and lacing between apices)
Measures (edge length 1)
Circumradius2
Hypervolume
Diteral anglesTip–tet–tepe:
 Grip–trip–tepe:
 Grip–tut–tip:
 Grip–toe–grip:
Central density1
Number of external pieces27
Level of complexity20
Related polytopes
ArmyGarx
RegimentGarx
DualTriangular-pyramidal pyramidal hecatonicosateron
ConjugateNone
Abstract & topological properties
Flag count14400
Euler characteristic2
OrientableYes
Properties
SymmetryA5, order 720
ConvexYes
NatureTame

The cantitruncated 5-simplex, also called the great rhombated hexateron or garx, is a convex uniform 5-polytope. It consists of 15 tetrahedral prisms, 6 truncated pentachora, and 6 great rhombated pentachora. One truncated pentachoron, 1 tetrahedral prism, and 3 great rhombated pentachora join at each vertex. As the name suggests, it is the cantitruncation of the 5-simplex.

Vertex coordinates[edit | edit source]

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

  • .

Representations[edit | edit source]

A cantitruncated 5-simplex has the following Coxeter diagrams:

  • x3x3x3o3o () (full symmetry)
  • xuxx3xxux3ooox3oooo&#xt (A4 axial, truncated pentachoron-first)

Gallery[edit | edit source]

External links[edit | edit source]