Cantellated 1 22 polytope

Cantellated 1 22 polytope
(OFF file)
Rank	6
Type	Uniform
Notation
Bowers style acronym	Sram
Coxeter diagram	o3x3o3x3o *c3x ()
Elements
Peta	720 triangular duoprismatic prisms, 72 small birhombidodecatera, 54 small birhombipenteractitriacontaditera
Tera	1440 triangular duoprisms, 4320 triangular-square duoprisms, 432+864 small rhombated pentachora, 270 rectified icositetrachora
Cells	4320+8640 triangular prisms, 2160 octahedra, 6480 cubes 2160+2160 cuboctahedra
Faces	2160+8640+8640 triangles, 12960+12960 squares
Edges	6480+25920
Vertices	6480
Vertex figure	Tetragonal disphenoidal pyramidal prism, edge lengths 1 (sides of prism and bases of disphenoid) and √2 (all other edges)
Measures (edge length 1)
Circumradius	${\sqrt {11}}\approx 3.31662$
Hypervolume	${\frac {7761{\sqrt {3}}}{4}}\approx 3360.61158$
Dipetal angles	Sibrid–triddip–tratrip: 150°
	Sibrant–tisdip–tratrip: 135°
	Sibrant–srip–sibrid: $\arccos \left(-{\frac {\sqrt {6}}{4}}\right)\approx 127.76124^{\circ }$
	Sibrant–rico–sibrant: 120°
	Sibrant–srip–sibrant: $\arccos \left(-{\frac {1}{4}}\right)\approx 104.47751^{\circ }$
Central density	1
Number of external pieces	846
Level of complexity	75
Related polytopes
Army	Sram
Regiment	Sram
Conjugate	None
Abstract & topological properties
Flag count	7776000
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	E6×2, order 103680
Convex	Yes
Nature	Tame

The cantellated 1 22 polytope or sram, also called the cantellated 1₂₂ polytope, is a convex uniform polypeton. It consists of 54 small birhombated penteracts, 72 small birhombidodecatera, and 720 triangular duoprismatic prisms. 4 small birhombated penteracts, 1 small birhombidodecateron, and 2 triangular duoprismatic prisms join at each vertex. As the name suggests, it is the cantellation of the pentacontatetrapeton.

Related polytopes

The regiment of the small rhombated pentacontatetrapeton contains 287 uniform members.

External links

• Klitzing, Richard. "sram".