Bicantitruncated 5-simplex

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Bicantitruncated 5-simplex
Rank5
TypeUniform
Notation
Bowers style acronymGibrid
Coxeter diagramo3x3x3x3o ()
Elements
Tera20 triangular duoprisms, 12 great rhombated pentachora
Cells120 triangular prisms, 30 truncated tetrahedra, 30 truncated octahedra
Faces120 triangles, 180 squares, 120 hexagons
Edges90+360
Vertices180
Vertex figureTetragonal disphenoidal pyramid, edge lengths 1 (base edges of disphenoid), 2 (sides of disphenoid), and 3 (sides of pyramid)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesGrip–trip–triddip:
 Grip–toe–grip:
 Grip–tut–grip:
Central density1
Number of external pieces32
Level of complexity15
Related polytopes
ArmyGibrid
RegimentGibrid
DualDisphenoidal pyramidal hecatonoctacontateron
ConjugateNone
Abstract & topological properties
Flag count21600
Euler characteristic2
OrientableYes
Properties
SymmetryA5×2, order 1440
ConvexYes
NatureTame

The bicantitruncated 5-simplex, also called the great birhombated hexateron, great birhombidodecateron, or gibrid, is a convex uniform 5-polytope. It consists of 20 triangular duoprisms and 12 great rhombated pentachora. 1 triangular duoprism and 4 great rhombated pentachora join at each vertex. As the name suggests, it is the bicantitruncation of the 5-simplex. It is also the truncation of the birectified 5-simplex.

Vertex coordinates[edit | edit source]

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

  • .

Representations[edit | edit source]

A bicantitruncated 5-simplex has the following Coxeter diagrams:

  • o3x3x3x3o () (full symmetry)
  • xooo3xuxx3xxux3ooox&#xt (A4 axial, great rhombated pentachoron-first)

Gallery[edit | edit source]

External links[edit | edit source]