Bicantitruncated 5-cube

Bicantitruncated 5-cube
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Gibrant
Coxeter diagram	o4x3x3x3o ()
Elements
Tera	80 triangular-square duoprisms, 32 great rhombated pentachora, 10 truncated icositetrachora
Cells	320 triangular prisms, 240 cubes, 80 truncated tetrahedra, 40+160 truncated octahedra
Faces	320 triangles, 240+960 squares, 320+320 hexagons
Edges	480+960+960
Vertices	960
Vertex figure	Digonal disphenoidal pyramid, edge lengths 1 (base 1 of dispehnoid), √2 (other edges of base), and √3 (sides of pyramid)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {46}}{2}}\approx 3.39117$
Hypervolume	${\frac {7513{\sqrt {2}}}{10}}\approx 1062.49865$
Diteral angles	Tico–cube–tisdip: $\arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }$
	Grip–trip–tisdip: $\arccos \left(-{\frac {\sqrt {15}}{5}}\right)\approx 140.76848^{\circ }$
	Grip–tut–grip: $\arccos \left(-{\frac {3}{5}}\right)\approx 126.86990^{\circ }$
	Tico–toe–grip: $\arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }$
	Tico–toe–tico: 90°
Central density	1
Number of external pieces	122
Level of complexity	30
Related polytopes
Army	Gibrant
Regiment	Gibrant
Dual	Disphenoidal pyramidal enneacosihexecontateron
Conjugate	None
Abstract & topological properties
Flag count	115200
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B5, order 3840
Convex	Yes
Nature	Tame

The bicantitruncated 5-cube, also called the great birhombated penteractitriacontaditeron, great birhombipenteractitriacontaditeron, or gibrant, is a convex uniform 5-polytope. It consists of 80 triangular-square duoprisms, 32 great rhombated pentachora, and 10 truncated icositetrachora. 1 triangular-square duoprism, 2 great rhombated pentachora, and 2 truncated icositetrachora join at each vertex. As the name suggests, it is the bicantitruncation of the 5-cube, or equivalently of its dual 5-orthoplex.

Vertex coordinates

The vertices of a bicantitruncated 5-cube of edge length 1 are given by all permutations of:

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

Representations

A bicantitruncated 5-cube has the following Coxeter diagrams:

• o4x3x3x3o () (full symmetry)
• x3x3x3o *b3x () (D₅ symmetry, as cantitruncate demipenteract)
• s4x3x3x3o () (D₅ symmetry, as alternated faceting)

Gallery

• 

  B₄ or D₅ orthographic projection

• 

  B₃, D₄, or A₂

• 

  B₂

• 

  A₃

External links

• Bowers, Jonathan. "Category 10: Greater Truncates" (#730).

• Klitzing, Richard. "gibrant".
• Wikipedia contributors. "Bicantitruncated 5-cube".