Bitruncated 5-cube

Bitruncated 5-cube
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Bittin
Coxeter diagram	o4x3x3o3o ()
Elements
Tera	32 truncated pentachora, 10 tesseractihexadecachora
Cells	80 tetrahedra, 160 truncated tetrahedra, 40 truncated octahedra
Faces	320 triangles, 80 squares, 320 hexagons
Edges	320+480
Vertices	320
Vertex figure	Triangular scalene, edge lengths 1 (base triangle), √2 (top edge), and √3 (sides)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {26}}{2}}\approx 2.54951$
Hypervolume	${\frac {1801{\sqrt {2}}}{15}}\approx 169.79991$
Diteral angles	Tip–tet–tip: $\arccos \left(-{\frac {3}{5}}\right)\approx 126.86990^{\circ }$
	Tip–tut–tah: $\arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }$
	Tah–toe–tah: 90°
Central density	1
Number of external pieces	42
Level of complexity	10
Related polytopes
Army	Bittin
Regiment	Bittin
Dual	Triangular-scalenic triacosiicosateron
Conjugate	None
Abstract & topological properties
Flag count	38400
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B5, order 3840
Flag orbits	10
Convex	Yes
Nature	Tame

The bitruncated 5-cube, also called the bitruncated penteract or bittin, is a convex uniform 5-polytope. It consists of 32 truncated pentachora and 10 tesseractihexadecachora. 2 truncated pentachora and 4 tesseractihexadecachora join at each vertex. As the name suggests, it is the bitruncation of the 5-cube.

Vertex coordinates

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

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

Representations

A bitruncated 5-cube has the following Coxeter diagrams:

• o4x3x3o3o () (full symmetry)
• x3x3o3o *b3x () (D₅ symmetry)
• s4x3x3o3o () (D₅ symmetry, as alternated faceting)
• ooqoo4xuxux3xooox3ooooo&#xt (B₄ axial, tesseractihexadecachoron-first)

Gallery

• 

  B₄ or D₅ orthographic projection

• 

  B₃, D₄, or A₂

• 

  B₂

• 

  A₃

External links

• Bowers, Jonathan. "Category 2: Truncates" (#22).

• Klitzing, Richard. "bittin".
• Wikipedia contributors. "Bitruncated 5-cube".