Great quasirhombated tesseract

Great quasirhombated tesseract
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Gaqrit
Coxeter diagram	x4/3x3x3o ()
Elements
Cells	32 triangular prisms, 16 truncated tetrahedra, 8 quasitruncated cuboctahedra
Faces	64 triangles, 96 squares, 64 hexagons, 24 octagrams
Edges	96+96+192
Vertices	192
Vertex figure	Sphenoid, edge lengths 1 (1), √2 (2), √3 (2), and √2–√2 (1)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {11-5{\sqrt {2}}}{2}}}\approx 1.40159$
Hypervolume	${\frac {601-424{\sqrt {2}}}{6}}\approx 0.22891$
Dichoral angles	Quitco–4–trip: $\arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }$
	Quitco–8/3–quitco: 90°
	Quitco–6–tut: 60°
	Tut–3–trip: 30°
Number of external pieces	512
Level of complexity	80
Related polytopes
Army	Semi-uniform Grit, edge lengths ${\sqrt {2}}-1$ (octagons), $2-{\sqrt {2}}$ (triangles)
Regiment	Gaqrit
Conjugate	Great rhombated tesseract
Convex core	Semi-uniform truncated hexadecachoron
Abstract & topological properties
Flag count	4608
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B4, order 384
Convex	No
Nature	Tame

The great quasirhombated tesseract, or gaqrit, is a nonconvex uniform polychoron that consists of 32 triangular prisms, 16 truncated tetrahedra, and 8 quasitruncated cuboctahedra. 1 triangular prism, 1 truncated tetrahedron, and 2 quasitruncated cuboctahedra join at each vertex. As the name suggests, it can be obtained by quasicantitruncating the tesseract.

Gallery

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  Vertices and edges

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  Cross-sections

Vertex coordinates

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

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

External links

• Bowers, Jonathan. "Category 8: Great Rhombates" (#315).

• Klitzing, Richard. "gaqrit".