Great disprismatotesseractihexadecachoron

From Polytope Wiki
Jump to navigation Jump to search
Great disprismatotesseracti-hexadecachoron
Schlegel half-solid omnitruncated 8-cell.png
Bowers style acronymGidpith
Coxeter diagramCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
Cells32 hexagonal prisms, 24 octagonal prisms, 16 truncated octahedra, 8 great rhombicuboctahedra
Faces96+96+96 squares, 64+64 hexagons, 48 octagons
Vertex figureIrregular tetrahedron, edge lengths 2 (3), 3 (2), and 2+2 (1) Omnitruncated 8-cell verf.png
Measures (edge length 1)
Dichoral anglesToe–6–hip: 150°
 Toe–4–op: 135°
 Girco–8–op: 135°
 Girco–6–toe: 120°
Central density1
Number of pieces80
Level of complexity24
Related polytopes
DualTetrahedral triacosioctacontatetrachoron
ConjugateGreat quasidisprismatotesseracti-hexadecachoron
Abstract properties
Euler characteristic0
Topological properties
SymmetryB4, order 384

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 BC4 family of uniform polychora.

The great disprismatotesseractihexadecachoron can be vertex-inscribed 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]

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 (BC3 axial, great rhombicuboctahedron-first)
  • wx3xx3xw *b3xx&#zx (D4 symmetry)

Semi-uniform variant[edit | edit source]

The great disprismatotesseractihexadecachoron has a semi-uniform 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.

o4o3o3o truncations
Name OBSA CD diagram Picture
Tesseract tes x4o3o3o
Schlegel wireframe 8-cell.png
Truncated tesseract tat x4x3o3o
Schlegel half-solid truncated tesseract.png
Rectified tesseract rit o4x3o3o
Schlegel half-solid rectified 8-cell.png
Tesseractihexadecachoron tah o4x3x3o
Schlegel half-solid bitruncated 8-cell.png
Rectified hexadecachoron = Icositetrachoron ico o4o3x3o
Schlegel half-solid rectified 16-cell.png
Truncated hexadecachoron thex o4o3x3x
Schlegel half-solid truncated 16-cell.png
Hexadecachoron hex o4o3o3x
Schlegel wireframe 16-cell.png
Small rhombated tesseract srit x4o3x3o
Schlegel half-solid cantellated 8-cell.png
Great rhombated tesseract grit x4x3x3o
Schlegel half-solid cantitruncated 8-cell.png
Small rhombated hexadecachoron = Rectified icositetrachoron rico o4x3o3x
Schlegel half-solid cantellated 16-cell.png
Great rhombated hexadecachoron = Truncated icositetrachoron tico o4x3x3x
Schlegel half-solid cantitruncated 16-cell.png
Small disprismatotesseractihexadecachoron sidpith x4o3o3x
Schlegel half-solid runcinated 8-cell.png
Prismatorhombated hexadecachoron proh x4x3o3x
Schlegel half-solid runcitruncated 8-cell.png
Prismatorhombated tesseract prit x4o3x3x
Schlegel half-solid runcitruncated 16-cell.png
Great disprismatotesseractihexadecachoron gidpith x4x3x3x
Schlegel half-solid omnitruncated 8-cell.png

External links[edit | edit source]