Cantitruncated 2 21 polytope

Cantitruncated 2 21 polytope
(OFF file)
Rank	6
Type	Uniform
Notation
Bowers style acronym	Girjak
Coxeter diagram	x3x3x3o3o *c3o ()
Elements
Peta	216 rectified pentachoric prisms 72 great rhombated hexatera 27 truncated demipenteracts 27 great rhombated triacontaditera
Tera	1080 tetrahedral prisms 432 rectified pentachora 1080 octahedral prisms 432 truncated pentachora 270 truncated hexadecachora 216+432 great rhombated pentachora
Cells	2160 tetrahedra 2160+4320 triangular prisms 2160 octahedra 1080+2160 truncated tetrahedra 1080 truncated octahedra
Faces	4320+8640 triangles, 6480 squares, 720+4320 hexagons
Edges	2160+2160+12960
Vertices	4320
Vertex figure	Triangular prismatic pyramidal pyramid, edge lengths 1 (base), √2 (sides of pyramid 1), and √3 (sides of pyramid 2 and lacing between apices)
Measures (edge length 1)
Circumradius	${\sqrt {13}}\approx 3.60555$
Hypervolume	${\frac {437799{\sqrt {3}}}{160}}\approx 4739.31320$
Dipetal angles	Thin–rap–rappip: $\arccos \left(-{\frac {\sqrt {10}}{4}}\right)\approx 142.23876^{\circ }$
	Garx–tepe–rappip: $\arccos \left(-{\frac {\sqrt {15}}{5}}\right)\approx 140.76848^{\circ }$
	Gart–ope–rappip: $\arccos \left(-{\frac {\sqrt {10}}{5}}\right)\approx 129.23152^{\circ }$
	Gart–grip–garx: $\arccos \left(-{\frac {\sqrt {6}}{4}}\right)\approx 127.76124^{\circ }$
	Thin–tip–garx: $\arccos \left(-{\frac {\sqrt {6}}{4}}\right)\approx 127.76124^{\circ }$
	Gart–thex–thin: 120°
	Gart–grip–gart: $\arccos \left(-{\frac {1}{4}}\right)\approx 104.47751^{\circ }$
Central density	1
Number of external pieces	342
Level of complexity	90
Related polytopes
Army	Girjak
Regiment	Girjak
Conjugate	None
Abstract & topological properties
Flag count	4665600
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	E6, order 51840
Convex	Yes
Nature	Tame

The cantitruncated 2 21 polytope or girjak, also called the cantitruncated 2₂₁ polytope, is a convex uniform polypeton. It consists of 27 great rhombated triacontaditera, 27 truncated demipenteracts, 72 great rhombated hexatera, and 216 rectified pentachoric prisms. 3 great rhombated triacontaditera, 1 truncated demipenteract, 2 great rhombated hexatera, and 1 rectified pentachoric prism join at each vertex. As the name suggests, it is the cantitruncation of the icosiheptaheptacontadipeton.

Related polytopes

The regiment of the cantitruncated 2 21 polytope contains two other uniform memmbers.

External links

• Klitzing, Richard. "girjak".