Great rhombated tesseractic prism

Great rhombated tesseractic prism
File:Great rhombated tesseractic prism.png
Rank	5
Type	Uniform
Notation
Bowers style acronym	Grittip
Coxeter diagram	x x43x3o
Elements
Tera	32 triangular-square duoprisms, 16 octahedral prisms, 8 great rhombicuboctahedral prisms, 2 great rhombated tesseracts
Cells	64+64 triangular prisms, 96 cubes, 64 hexagonal prisms, 32 truncated tetrahedra, 24 octagonal prisms, 16 great rhombicuboctahedra
Faces	128 triangles, 96+96+192+192 squares, 128 hexagons, 48 octagons
Edges	192+192+192+384
Vertices	384
Vertex figure	Sphenoidal pyramid, edge lengths 1, √2, √3, √2+√2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {23+10{\sqrt {2}}}}{2}}\approx 3.04722$
Hypervolume	${\frac {601+424{\sqrt {2}}}{6}}\approx 200.10443$
Diteral angles	Tuttip–trip–tisdip: 150°
	Gircope–cube–tisdip: $\arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }$
	Gircope–hip–tuttip: 120°
	Gircope–op–gircope: 90°
	Grit–girco–gircope: 90°
	Grit–tut–tuttip: 90°
	Grit–trip–tisdip: 90°
Height	1
Central density	1
Number of external pieces	58
Level of complexity	60
Related polytopes
Army	Grittip
Regiment	Grittip
Dual	Sphenoidal hecatonenneacontadichoric tegum
Conjugate	Great quasirhombated tesseractic prism
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B4×A1, order 768
Convex	Yes
Nature	Tame

The great rhombated tesseractic prism or grittip is a prismatic uniform polyteron that consists of 2 great rhombated tesseracts, 8 great rhombicuboctahedral prisms, 16 truncated tetrahedral prisms, and 32 triangular-square duoprisms. 1 great rhombated tesseract, 2 great rhombicuboctahedral prisms, 1 truncated tetrahedral prism, and 1 triangular-square duoprism join at each vertex. As the name suggests, it is a prism based on the great rhombated tesseract, which also makes it a convex segmentoteron.

The great rhombated tesseractic prism can be vertex-inscribed into the prismatorhombated penteract.

Vertex coordinates

The vertices of a great rhombated tesseractic prism of edge length 1 are given by all permutations and sign changes of the first four coordinates of:

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

External links

• Klitzing, Richard. "Grittip".