Great disprismatotesseractihexadecachoron
Great disprismatotesseractihexadecachoron  

Rank  4 
Type  Uniform 
Notation  
Bowers style acronym  Gidpith 
Coxeter diagram  x4x3x3x () 
Elements  
Cells  32 hexagonal prisms, 24 octagonal prisms, 16 truncated octahedra, 8 great rhombicuboctahedra 
Faces  96+96+96 squares, 64+64 hexagons, 48 octagons 
Edges  192+192+192+192 
Vertices  384 
Vertex figure  Irregular tetrahedron, edge lengths √2 (3), √3 (2), and √2+√2 (1) 
Measures (edge length 1)  
Circumradius  
Hypervolume  
Dichoral angles  Toe–6–hip: 150° 
Op–4–hip:  
Toe–4–op: 135°  
Girco–8–op: 135°  
Girco–4–hip:  
Girco–6–toe: 120°  
Central density  1 
Number of external pieces  80 
Level of complexity  24 
Related polytopes  
Army  Gidpith 
Regiment  Gidpith 
Dual  Tetrahedral triacosioctacontatetrachoron 
Conjugate  Great quasidisprismatotesseractihexadecachoron 
Abstract & topological properties  
Flag count  9216 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  B_{4}, order 384 
Convex  Yes 
Nature  Tame 
The great disprismatotesseractihexadecachoron, or gidpith, also commonly called the omnitruncated tesseract or omnitruncated hexadecachoron, is a convex uniform polychoron that consists of 32 hexagonal prisms, 24 octagonal prisms, 16 truncated octahedra, and 8 great rhombicuboctahedra. 1 of each type of cell join at each vertex. It is the omnitruncate of the B_{4} family of uniform polychora.
The great disprismatotesseractihexadecachoron can be vertexinscribed into a prismatorhombated icositetrachoron.
This polychoron can be alternated into a snub tesseract, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a pyritosnub tesseract, which is also nonuniform. If the octagons are alternated alternately, then the resulting polychoron is a truncated icositetrachoron.
Gallery[edit  edit source]

B4 Coxeter plane projection

Stereographic projection

Net

Crosssection animation
Vertex coordinates[edit  edit source]
Vertex coordinates for a great disprismatotesseractihexadecachoron of edge length 1 are given by all permutations of:
 .
Representations[edit  edit source]
A great disprismatotesseractihexadecachoron has the following Coxeter diagrams:
 x4x3x3x () (full symmetry)
 xxxwwxxx4xxuxxuxx3xuxxxxux&#xt (B_{3} axial, great rhombicuboctahedronfirst)
 wx3xx3xw *b3xx&#zx (D_{4} symmetry)
Semiuniform variant[edit  edit source]
The great disprismatotesseractihexadecachoron has a semiuniform variant of the form a4b3c3d that maintains its full symmetry. This variant uses 8 great rhombicuboctahedra of form a4b3c, 16 great rhombitetratetrahedra of form b3c3d, 24 ditetragonal prisms of form d a4b, and 32 ditrigonal prisms of form a c3d as cells, with 4 edge lengths.
With edges of length a, b, c, and d (such that it forms a4b3c3d), its circumradius is given by .
It has coordinates given by all permutations of:
 .
Related polychora[edit  edit source]
A great disprismatotesseractihexadecachoron can be augmented by joining truncated octahedron atop great rhombicuboctahedron segmentochora to its great rhombicuboctahedral cells. If all eight great rhombicuboctahedra are augmented, the result is the prismatorhombated icositetrachoron, as the octagonal prisms merge with square cupolas coming from the augments.
External links[edit  edit source]
 Bowers, Jonathan. "Category 9: Omnitruncates" (#331).
 Bowers, Jonathan. "Tessic Isogonals".
 Klitzing, Richard. "gidpith".
 Quickfur. "The Omnitruncated Tesseract".
 Wikipedia contributors. "Omnitruncated tesseract".