Great quasirhombated penteract
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Great quasirhombated penteract | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Gaqrin |
Coxeter diagram | x4/3x3x3o3o () |
Elements | |
Tera | 80 tetrahedral prisms, 32 truncated pentachora, 10 great quasirhombated tesseracts |
Cells | 160 tetrahedra, 320 triangular prisms, 160 truncated tetrahedra, 40 quasitruncated cuboctahedra |
Faces | 640 triangles, 480 squares, 320 hexagons, 80 octagrams |
Edges | 320+320+960 |
Vertices | 640 |
Vertex figure | Triangular 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 angles | Gaqrit–trip–tepe: 120° |
Gaqrit–quitco–gaqrit: 90° | |
Gaqrit–tut–tip: | |
Tip–tet–tepe: | |
Related polytopes | |
Army | Semi-uniform Girn, edge lengths (octagons), (tetrahedra) |
Regiment | Gaqrin |
Conjugate | Great rhombated penteract |
Abstract & topological properties | |
Flag count | 76800 |
Orientable | Yes |
Properties | |
Symmetry | B5, order 3840 |
Convex | No |
Nature | Tame |
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]
- Bowers, Jonathan. "Category 10: Greater Truncates" (#726).
- Klitzing, Richard. "gaqrin".