Bicantitruncated 6-orthoplex
Bicantitruncated 6-orthoplex | |
---|---|
Rank | 6 |
Type | Uniform |
Notation | |
Bowers style acronym | Gaborg |
Coxeter diagram | o4o3x3x3x3o () |
Elements | |
Peta | 160 triangular-octahedral duoprisms 64 bicantitruncated 5-simplices 12 cantitruncated 5-orthoplexes |
Tera | 1280 triangular duoprisms 480 octahedral prisms 60 truncated hexadecachora 192+384 great rhombated pentachora |
Cells | 1920+3840 triangular prisms 480 octahedra 240+960 truncated tetrahedra 960 truncated octahedra |
Faces | 960+3840 triangles, 5760 squares, 960+1920 hexagons |
Edges | 1440+2880+5760 |
Vertices | 2880 |
Vertex figure | Square 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 angles | Gart–ope–troct: |
Gibrid–triddip–troct: 135° | |
Gibrid–grip–gibrid: | |
Gart–grip–gibrid: | |
Gart–thex–gart: 90° | |
Central density | 1 |
Number of external pieces | 236 |
Level of complexity | 60 |
Related polytopes | |
Army | Gaborg |
Regiment | Gaborg |
Conjugate | None |
Abstract & topological properties | |
Flag count | 2764800 |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | B6, order 46080 |
Convex | Yes |
Nature | Tame |
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]
-
B5 orthographic projection
-
B4
-
B3
-
B2
-
A5
-
A3
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]
- Klitzing, Richard. "gaborg".
- Wikipedia contributors. "Bicantitruncated 6-orthoplex".