Great quasiprismatotetracontoctachoron

Great quasiprismatotetracontoctachoron
	(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Gaquapac
Coxeter diagram	x3x4/3x3x ()
Elements
Cells	192 hexagonal prisms, 48 quasitruncated cuboctahedra
Faces	288+576 squares, 384 hexagons, 144 octagrams
Edges	1152+1152
Vertices	1152
Vertex figure	Phyllic disphenoid, edge lengths √2 (3), √3 (2), and √2–√2 (1)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Quitco–6–hip: 150°
	Quitco–4–hip:
	Quitco–8/3–quitco: 45°
	Hip–4–hip:
Central density	73
Number of external pieces	145728
Level of complexity	3178
Related polytopes
Army	Semi-uniform Gippic, edge lengths (octagons), (remaining edges)
Regiment	Gaquapac
Conjugate	Great prismatotetracontoctachoron
Convex core	Bijungatotetracontoctachoron
Abstract & topological properties
Flag count	27648
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	F4×2, order 2304
Convex	No
Nature	Tame

The great quasiprismatotetracontoctachoron, or gaquapac, is a nonconvex uniform polychoron that consists of 192 hexagonal prisms and 48 quasitruncated cuboctahedra. 2 of each join at each vertex.

Gallery[edit | edit source]

The vertices of a great quasiprismatotetracontoctachoron of edge length 1 are given by all permutations of:

$\left(\pm {\frac {5-3{\sqrt {2}}}{2}},\,\pm {\frac {2{\sqrt {2}}-1}{2}},\,\pm {\frac {{\sqrt {2}}-1}{2}},\,\pm {\frac {1}{2}}\right),$
$\left(\pm 3{\frac {{\sqrt {2}}-1}{2}},\,\pm {\frac {3-2{\sqrt {2}}}{2}},\,\pm {\frac {3-{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}}\right),$
$\left(\pm {\frac {3{\sqrt {2}}-4}{2}},\,\pm ({\sqrt {2}}-1),\,\pm {\frac {2-{\sqrt {2}}}{2}},\,\pm 1\right).$