Great rhombated pentacontatetrapeton

Great rhombated pentacontatetrapeton
Rank	6
Type	Uniform
Notation
Bowers style acronym	Gram
Coxeter diagram	o3x3x3x3o *c3x ()
Elements
Peta	54 great birhombipenteractitriacontaditera 72 great birhombidodecatera 720 triangular duoprismatic prisms
Tera	1440 triangular duoprisms 4320 triangular-square duoprisms 432+864 great rhombated pentachora 270 truncated icositetrachora
Cells	4320+8640 triangular prisms 6480 cubes 2160 truncated tetrahedra 2160+2160 truncated octahedra
Faces	8640 triangles, 12960+12960 squares, 2160+8640 hexagons
Edges	6480+6480+25920
Vertices	12960
Vertex figure	Irregular hexateron
Measures (edge length 1)
Circumradius	5
Hypervolume	${\frac {177117{\sqrt {3}}}{8}}\approx 38346.95536$
Central density	1
Number of external pieces	846
Related polytopes
Army	Gram
Regiment	Gram
Conjugate	None
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	E6×2, order 103680
Convex	Yes
Nature	Tame

The great rhombated pentacontatetrapeton or gram, also called the cantitruncated 1₂₂ polytope, is a convex uniform polypeton. It consists of 54 great birhombated penteracts, 72 great birhombidodecatera, and 720 triangular duoprismatic prisms. 4 great birhombated penteracts, 1 great birhombidodecateron, and 1 triangular duoprismatic prism join at each vertex. As the name suggests, it is the cantitruncation of the pentacontatetrapeton.

External links

• Klitzing, Richard. "gram".