Bicantitruncated 6-orthoplex

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Bicantitruncated 6-orthoplex
Rank6
TypeUniform
Notation
Bowers style acronymGaborg
Coxeter diagramo4o3x3x3x3o ()
Elements
Peta160 triangular-octahedral duoprisms
64 bicantitruncated 5-simplices
12 cantitruncated 5-orthoplexes
Tera1280 triangular duoprisms
480 octahedral prisms
60 truncated hexadecachora
192+384 great rhombated pentachora
Cells1920+3840 triangular prisms
480 octahedra
240+960 truncated tetrahedra
960 truncated octahedra
Faces960+3840 triangles, 5760 squares, 960+1920 hexagons
Edges1440+2880+5760
Vertices2880
Vertex figureSquare pyramidal scalene, edge lengths 1 (square and top dyad), 2 (lacings between square and dyad), and 3 (remaining lacings)
Measures (edge length 1)
Circumradius
Hypervolume
Dipetal anglesGart–ope–troct:
 Gibrid–triddip–troct: 135°
 Gibrid–grip–gibrid:
 Gart–grip–gibrid:
 Gart–thex–gart: 90°
Central density1
Number of external pieces236
Level of complexity60
Related polytopes
ArmyGaborg
RegimentGaborg
ConjugateNone
Abstract & topological properties
Flag count2764800
Euler characteristic0
OrientableYes
Properties
SymmetryB6, order 46080
ConvexYes
NatureTame

The bicantitruncated 6-orthoplex, also called the bicantitruncated hexacontatetrapeton, great birhombated hexacontatetrapeton, or gaborg, is a convex uniform 6-polytope. It consists of 12 cantitruncated 5-orthoplexes, 64 bicantitruncated 5-simplices, and 160 triangular-octahedral duoprisms. 2 cantitruncated 5-orthoplexes, 4 bicantitruncated 5-simplices, and 1 triangular-octahedral duoprism join at each vertex. As the name suggests, it is the bicantitruncation of the 6-orthoplex.

Vertex coordinates[edit | edit source]

The coordinates of a bicantitruncated 6-orthoplex, centered at the origin and with unit edge length, are given by all permutations of:

  • .

Representations[edit | edit source]

A bicantitruncated 6-orthoplex has the following Coxeter diagrams:

  • o4o3x3x3x3o () (full symmetry)
  • o3x3x3x3o *b3o () (D6 symmetry)

Gallery[edit | edit source]

Related polytopes[edit | edit source]

The bicantitruncated 6-orthoplex is the colonel of a two-member regiment that also includes the great birhombated triacontadihemihexeract.

External links[edit | edit source]