(Redirected from Gittith)
Rank4
TypeUniform
Notation
Bowers style acronymGittith
Coxeter diagramo3o3x4/3x4*b ()
Elements
Cells16 tetrahedra, 8 cubes, 8 great cubicuboctahedra
Faces64 triangles, 48 squares, 24 octagrams
Edges96+96
Vertices64
Vertex figureTriangular frustum, edge lengths 1 (small base), 2 (large base), and 2–2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {3-{\sqrt {2}}}{2}}}\approx 0.89045}$
Hypervolume${\displaystyle {\frac {24{\sqrt {2}}-19}{6}}\approx 2.49019}$
Dichoral anglesGocco–3–tet: 120°
Gocco–8/3–gocco: 90°
Gocco–4–cube: 90°
Central density5
Number of external pieces152
Level of complexity30
Related polytopes
ArmyTat, edge length ${\displaystyle {\sqrt {2}}-1}$
RegimentGittith
Abstract & topological properties
Flag count2304
Euler characteristic–24
OrientableYes
Properties
SymmetryB4, order 384
ConvexNo

The great tesseractitesseractihexadecachoron, or gittith, is a nonconvex uniform polychoron that consists of 16 regular tetrahedra, 8 cubes, and 8 great cubicuboctahedra. 1 tetrahedron, 1 cube, and 3 great cubicuboctahedra join at each vertex.

The great tesseractitesseractihexadecachoron contains the vertices and edges of a great cubicuboctahedral prism and square-octagrammic duoprism.

## Vertex coordinates

Coordinates for the vertices of a great tesseractitesseractihexadecachoron with edge length 1 are given by all permutations of:

• ${\displaystyle \left(\pm {\frac {{\sqrt {2}}-1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right).}$

## Related polychora

The great tesseractitesseractihexadecachoron is the colonel of a regiment with a total of 8 uniform and 6 scaliform members. Of these members, 7 have full tesseractic symmetry, namely gittith, quidpith, picnut, gittifcoth, gahfipto, gnappoth, and gnipto. The eighth member, gaquipadah, has square duoprism symmetry, as do the 6 scaliform members. The compound octagrammic diorthoprism can be edge-inscribed in this polychoron.