Prismatorhombated tesseract
Prismatorhombated tesseract  

Rank  4 
Type  Uniform 
Notation  
Bowers style acronym  Prit 
Coxeter diagram  x4o3x3x () 
Elements  
Cells  24 cubes, 32 hexagonal prisms, 16 truncated tetrahedra, 8 small rhombicuboctahedra 
Faces  64 triangles, 48+96+96 squares, 64 hexagons 
Edges  96+192+192 
Vertices  192 
Vertex figure  Isosceles trapezoidal pyramid, base edge lengths 1, √2, √2, √2; lateral edge lengths √2, √2, √3, √3 
Measures (edge length 1)  
Circumradius  
Hypervolume  
Dichoral angles  Tut–6–hip: 150° 
Hip–4–cube:  
Sirco–4–cube: 135°  
Sirco–4–hip:  
Sirco–3–tut: 120°  
Central density  1 
Number of external pieces  80 
Level of complexity  16 
Related polytopes  
Army  Prit 
Regiment  Prit 
Dual  Deltopyramidal hecatonenneacontadichoron 
Conjugate  Prismatoquasirhombated tesseract 
Abstract & topological properties  
Flag count  6144 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  B_{4}, order 384 
Flag orbits  16 
Convex  Yes 
Nature  Tame 
The prismatorhombated tesseract, or prit, also commonly called the runcitruncated 16cell, is a convex uniform polychoron that consists of 24 cubes, 32 hexagonal prisms, 16 truncated tetrahedra, and 8 small rhombicuboctahedra. 1 cube, 2 hexagonal prisms, 1 truncated tetrahedron, and 1 small rhombicuboctahedron join at each vertex. As one of its names suggests, it can be obtained by runcitruncating the hexadecachoron.
Gallery[edit  edit source]

B4 Coxeter plane projection

Net
Vertex coordinates[edit  edit source]
The vertices of a prismatorhombated tesseract of edge length 1 are given by all permutations of:
 .
Representations[edit  edit source]
A prismatorhombated tesseract has the following Coxeter diagrams:
 x4o3x3x () (full symmetry)
 xxxxxx4ooxxoo3xuxxux&#xt (B_{3} axial, small rhombicuboctahedronfirst)
 qo3xx3oq *b3xx&#zx (D_{4} symmetry)
 Xwx xxx4oox3xux&#zx (B_{3}×A_{1} symmetry)
Semiuniform variant[edit  edit source]
The prismatorhombated tesseract has a semiuniform variant of the form x4o3y3z that maintains its full symmetry. This variant uses 8 small rhombicuboctahedra of form x4o3y, 16 truncated tetrahedra of form z3y3o, 24 square prisms of form z x4o, and 32 ditrigonal prisms of form x y3z as cells, with 3 edge lengths.
With edges of length a, b, and c (such that it forms a4o3b3c), its circumradius is given by .
It has coordinates given by all permutations of:
 .
Related polychora[edit  edit source]
The prismatorhombated tesseract is the colonel of a 3member regiment that also includes the small cubihexadecadisoctachoron and the small rhombiprismic disoctachoron.
The great rhombicuboctahedral prism can be obtained as the central segment of the prismatorhombated tesseract in small rhombicuboctahedronfirst orientation.
Uniform polychoron compounds composed of prismatorhombated tesseracts include:
 Prismatorhombated great icositetrachoron (3)
 Prismatorhombated great stellated tetracontoctachoron (6)
 Prismatorhombated dodecahedronary hexacosichoron (75)
External links[edit  edit source]
 Bowers, Jonathan. "Category 10: Prismatorhombates" (#355).
 Bowers, Jonathan. "Tessic Isogonals".
 Klitzing, Richard. "prit".
 Quickfur. "The Runcitruncated 16cell".
 Wikipedia contributors. "Runcitruncated 16cell".