Bicantellated 6-simplex

Bicantellated 6-simplex
(OFF file)
Rank	6
Type	Uniform
Notation
Bowers style acronym	Sabril
Coxeter diagram	o3x3o3x3o3o ()
Elements
Peta	35 triangular-tetrahedral duoprisms 7 small rhombated hexatera 7 small birhombidodecatera
Tera	105 tetrahedral prisms 140 triangular duoprisms 21 rectified pentachora 21+42 small rhombated pentachora
Cells	105 tetrahedra 210+420 triangular prisms 35+105 octahedra 105 cuboctahedra
Faces	140+140+210+420 triangles, 630 squares
Edges	420+630
Vertices	210
Vertex figure	Triangular scalenic prism, edge lengths 1 (base triangular prism and top square), √2 (sides)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {119}}{7}}\approx 1.55839$
Hypervolume	${\frac {3163{\sqrt {7}}}{960}}\approx 8.71720$
Dipetal angles	Sarx–tepe–tratet: $\arccos \left(-{\frac {\sqrt {2}}{3}}\right)\approx 118.12551^{\circ }$
	Sibrid–triddip–tratet: $\arccos \left(-{\frac {\sqrt {2}}{4}}\right)\approx 110.70481^{\circ }$
	Sibrid–srip–sarx: $\arccos \left(-{\frac {1}{6}}\right)\approx 99.59407^{\circ }$
	Sibrid–srip–sibrid: $\arccos \left({\frac {1}{6}}\right)\approx 80.40593^{\circ }$
	Sarx–rap–sarx: $\arccos \left({\frac {1}{6}}\right)\approx 80.40593^{\circ }$
Central density	1
Number of external pieces	49
Level of complexity	50
Related polytopes
Army	Sabril
Regiment	Sabril
Conjugate	None
Abstract & topological properties
Flag count	252000
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A6, order 5040
Convex	Yes
Nature	Tame

The bicantellated 6-simplex (also called the bicantellated heptapeton, small birhombated heptapeton, or sabril) is a convex uniform 6-polytope. It consists of 7 small birhombidodecatera, 7 small rhombated hexatera, and 35 triangular-tetrahedral duoprisms as facets. 3 small birhombidodecatera, 2 small rhombated hexatera, and 2 triangular-tetrahedral duoprisms join at each vertex. As the name suggests, it is the bicantellation of the 6-simplex.

Gallery

• 

  A₅ orthographic projection

• 

  A₄

• 

  A₃

• 

  A₂

Vertex coordinates

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

• $\left({\sqrt {2}},\,{\sqrt {2}},\,{\frac {\sqrt {2}}{2}},\,{\frac {\sqrt {2}}{2}},\,0,\,0,\,0\right)$.

Related polytopes

The bicantellated 6-simplex is the colonel of a regiment of 63 uniform members.

External links

• Klitzing, Richard. "sabril".
• Wikipedia contributors. "Bicantellated 6-simplex".