Great quasirhombated icositetrachoron
Great quasirhombated icositetrachoron  

Rank  4 
Type  Uniform 
Notation  
Bowers style acronym  Gaqri 
Coxeter diagram  x3x4/3x3o () 
Elements  
Cells  96 triangular prisms, 24 quasitruncated hexahedra, 24 quasitruncated cuboctahedra 
Faces  192 triangles, 288 squares, 96 hexagons, 144 octagrams 
Edges  288+288+576 
Vertices  576 
Vertex figure  Sphenoid edge lengths 1 (1), √2 (2), √3 (1), and √2–√2 (2) 
Measures (edge length 1)  
Circumradius  
Hypervolume  
Dichoral angles  Quitco–6–quitco: 120° 
Quitco–8/3–quith: 45°  
Quitco–4–trip:  
Quith–3–trip: 30°  
Number of external pieces  2856 
Level of complexity  105 
Related polytopes  
Army  Semiuniform Prico, edge lengths (small rhombicuboctahedra), (bases of triangular prisms) 
Regiment  Gaqri 
Conjugate  Great rhombated icositetrachoron 
Convex core  Icositetrachoron 
Abstract & topological properties  
Flag count  13824 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  F_{4}, order 1152 
Convex  No 
Nature  Tame 
The great quasirhombated icositetrachoron, or gaqri, is a nonconvex uniform polychoron that consists of 96 triangular prisms, 24 quasitruncated hexahedra, and 24 quasitruncated cuboctahedra. 1 triangular prism, 1 quasitruncated hexahedron, and 2 quasitruncated cuboctahedra join at each vertex. As the name suggests, it can be obtained by quasicantitruncating the icositetrachoron.
Gallery[edit  edit source]

Crosssection animation

The vertices and edges of gaqri
Vertex coordinates[edit  edit source]
The vertices of a great quasirhombated icositetrachoron of edge length 1 are given by all permutations of:
The quasicantitruncation of the dual icositetrachron has coordinates given by all permutations of:
External links[edit  edit source]
 Bowers, Jonathan. "Category 8: Great Rhombates" (#316).
 Klitzing, Richard. "gaqri".