Great quasirhombated penteract

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Great quasirhombated penteract
Rank5
TypeUniform
Notation
Bowers style acronymGaqrin
Coxeter diagramx4/3x3x3o3o ()
Elements
Tera80 tetrahedral prisms, 32 truncated pentachora, 10 great quasirhombated tesseracts
Cells160 tetrahedra, 320 triangular prisms, 160 truncated tetrahedra, 40 quasitruncated cuboctahedra
Faces640 triangles, 480 squares, 320 hexagons, 80 octagrams
Edges320+320+960
Vertices640
Vertex figureTriangular pyramidal pyramid, edge lengths 1 (base), 2 (sides of pyramid 1), 3 (sides of pyramid 2), and 2–2 (lacing between apices)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesGaqrit–trip–tepe: 120°
 Gaqrit–quitco–gaqrit: 90°
 Gaqrit–tut–tip:
 Tip–tet–tepe:
Related polytopes
ArmySemi-uniform Girn, edge lengths (octagons), (tetrahedra)
RegimentGaqrin
ConjugateGreat rhombated penteract
Abstract & topological properties
Flag count76800
OrientableYes
Properties
SymmetryB5, order 3840
ConvexNo
NatureTame

The great quasirhombated penteract, or gaqrin, is a nonconvex uniform polyteron. It consists of 80 tetrahedral prisms, 32 truncated pentachora, and 10 great quasirhombated tesseracts. One truncated pentachoron, 1 tetrahedral prism, and 3 great quasirhombated tesseracts join at each vertex. It is the quasicantitruncation of the penteract.

Vertex coordinates[edit | edit source]

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

External links[edit | edit source]