Bitruncated 1 22 polytope

Bitruncated 1 22 polytope
(OFF file)
Rank	6
Type	Uniform
Notation
Bowers style acronym	Bitem
Coxeter diagram	o3x3x3x3o *c3o ()
Elements
Peta	72 bicantitruncated 5-simplices, 54 runcicantic 5-cubes
Tera	720 triangular duoprisms, 432 decachora, 864 great rhombated pentachora, 270 tesseractihexadecachora
Cells	4320 triangular prisms, 2160+2160 truncated tetrahedra, 2160 truncated octahedra
Faces	2160+4320 triangles, 6480 squares, 8640 hexagons
Edges	6480+12960
Vertices	6480
Vertex figure	Digonal trisphenoid, edge lengths 1 (3 base edges), √2 (one set of lacings), and √3 (other lacings)
Measures (edge length 1)
Circumradius	${\sqrt {17}}\approx 4.12311$
Hypervolume	${\frac {561321{\sqrt {3}}}{80}}\approx 12152.9561$
Dipetal angles	Girhin–grip–gibrid: $\arccos \left(-{\frac {\sqrt {6}}{4}}\right)\approx 127.76124^{\circ }$
	Gibrid–triddip–gibrid: 120°
	Girhin–tah–girhin: 120°
	Girhin–deca–girhin: $\arccos \left(-{\frac {1}{4}}\right)\approx 104.47751^{\circ }$
Central density	1
Number of external pieces	126
Level of complexity	45
Related polytopes
Army	Bitem
Regiment	Bitem
Conjugate	None
Abstract & topological properties
Flag count	4665600
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	E6×2, order 103680
Convex	Yes
Nature	Tame

The bitruncated 1₂₂ polytope, also called the bitruncated pentacontatetrapeton or bitem, is a convex uniform 6-polytope. It consists of 54 runcicantic 5-cubes and 72 bicantitruncated 5-simplices. 4 runcicantic 5-cubes and 2 bicantitruncated 5-simplices join at each vertex. As the name suggests, it is the bitruncation of the 1₂₂ polytope.

External links

• Klitzing, Richard. "bitem".