Great demiprismated icosiheptaheptacontadipeton

Great demiprismated icosiheptaheptacontadipeton
Rank	6
Type	Uniform
Notation
Bowers style acronym	Ghopjak
Coxeter diagram	x3x3x3x3o *c3o ()
Elements
Peta	72 great prismated hexatera 27 great prismatodemipenteracts 216 decachoric prisms 27 great rhombidemipenteracts
Tera	432 great prismatodecachora 216+432 great rhombated pentachora 720 triangular-hexagonal duoprisms 1080+1080 truncated tetrahedral prisms 270 truncated hexadecachora 432 decachora
Cells	1080+2160 truncated octahedra 2160+4320 hexagonal prisms 2160+2160+2160 triangular prisms 1080+2160+2160 truncated tetrahedra
Faces	2160+4320+8640 hexagons, 6480+6480+6480 squares, 4320+4320 triangles
Edges	6480+6480+12960+12960
Vertices	12960
Vertex figure	Irregular hexateron
Measures (edge length 1)
Circumradius	${\sqrt {\frac {68}{3}}}\approx 4.76095$
Hypervolume	${\frac {292327{\sqrt {3}}}{16}}\approx 31645.32603$
Central density	1
Number of external pieces	342
Related polytopes
Army	Ghopjak
Regiment	Ghopjak
Conjugate	None
Abstract & topological properties
Flag count	9331200
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	E6, order 51840
Convex	Yes
Nature	Tame

The great demiprismated icosiheptaheptacontadipeton or ghopjak, also called the demiruncicantitruncated 2₂₁ polytope, is a convex uniform polypeton. It consists of 27 great prismated demipenteracts, 27 great rhombated demipenteracts, 72 great prismated hexatera, and 216 decachoric prisms. 2 great prismated demipenteracts, 1 great rhombated demipenteract, 2 great prismated hexatera, and 1 decachoric prism join at each vertex.