Bicantitruncated 5-simplex

Bicantitruncated 5-simplex
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Gibrid
Coxeter diagram	o3x3x3x3o ()
Elements
Tera	20 triangular duoprisms, 12 great rhombated pentachora
Cells	120 triangular prisms, 30 truncated tetrahedra, 30 truncated octahedra
Faces	120 triangles, 180 squares, 120 hexagons
Edges	90+360
Vertices	180
Vertex figure	Tetragonal disphenoidal pyramid, edge lengths 1 (base edges of disphenoid), √2 (sides of disphenoid), and √3 (sides of pyramid)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {19}}{2}}\approx 2.17945$
Hypervolume	${\frac {2653{\sqrt {3}}}{80}}\approx 57.43913$
Diteral angles	Grip–trip–triddip: $\arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }$
	Grip–toe–grip: $\arccos \left(-{\frac {1}{5}}\right)\approx 101.53696^{\circ }$
	Grip–tut–grip: $\arccos \left({\frac {1}{5}}\right)\approx 78.46304^{\circ }$
Central density	1
Number of external pieces	32
Level of complexity	15
Related polytopes
Army	Gibrid
Regiment	Gibrid
Dual	Disphenoidal pyramidal hecatonoctacontateron
Conjugate	None
Abstract & topological properties
Flag count	21600
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	A5×2, order 1440
Convex	Yes
Nature	Tame

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

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

• $\left({\frac {3{\sqrt {2}}}{2}},\,{\frac {3{\sqrt {2}}}{2}},\,{\sqrt {2}},\,{\frac {\sqrt {2}}{2}},\,0,\,0\right)$.

Representations

A bicantitruncated 5-simplex has the following Coxeter diagrams:

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

Gallery

• 

  A₄ orthographic projection

• 

  A₃

• 

  A₂

External links

• Bowers, Jonathan. "Category 10: Greater Truncates" (#729).

• Klitzing, Richard. "gibrid".
• Wikipedia contributors. "Bicantitruncated 5-simplex".