Great tesseractitesseractihexadecachoron

Great tesseractitesseractihexadecachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Gittith
Coxeter diagram	o3o3x4/3x4*b ()
Elements
Cells	16 tetrahedra, 8 cubes, 8 great cubicuboctahedra
Faces	64 triangles, 48 squares, 24 octagrams
Edges	96+96
Vertices	64
Vertex figure	Triangular frustum, edge lengths 1 (small base), √2 (large base), and √2–√2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {3-{\sqrt {2}}}{2}}}\approx 0.89045$
Hypervolume	${\frac {24{\sqrt {2}}-19}{6}}\approx 2.49019$
Dichoral angles	Gocco–3–tet: 120°
	Gocco–8/3–gocco: 90°
	Gocco–4–cube: 90°
Central density	5
Number of external pieces	152
Level of complexity	30
Related polytopes
Army	Tat, edge length ${\sqrt {2}}-1$
Regiment	Gittith
Conjugate	Small tesseractitesseractihexadecachoron
Abstract & topological properties
Flag count	2304
Euler characteristic	–24
Orientable	Yes
Properties
Symmetry	B4, order 384
Convex	No

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.

Cross-sections

Vertex coordinates

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

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

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.

External links

• Bowers, Jonathan. "Category 12: Podiumverts" (#484).

• Klitzing, Richard. "gittith".