Truncated hexadecachoric prism

Truncated hexadecachoric prism
File:Truncated hexadecachoric prism.png
Rank	5
Type	Uniform
Notation
Bowers style acronym	Thexip
Coxeter diagram	x o4o3x3x ()
Elements
Tera	8 octahedral prisms, 16 truncated tetrahedral prisms, 2 truncated hexadecachora
Cells	64 triangular prisms, 32 hexagonal prisms, 16 octahedra, 32 truncated tetrahedra
Faces	128 triangles, 24+96 squares, 64 hexagons
Edges	48+48+192
Vertices	96
Vertex figure	Square pyramidal pyramid, edge lengths 1, √3 (base), √2 (legs)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {11}}{2}}\approx 1.65831$
Hypervolume	${\frac {7}{6}}\approx 12.83333$
Diteral angles	Ope–trip–tuttip: 120°
	Tuttip–hip–tuttip: 120°
	Thex-oct–ope: 90°
	Thex–tut–tuttip: 90°
Height	1
Central density	1
Number of external pieces	26
Level of complexity	20
Related polytopes
Army	Thexip
Regiment	Thexip
Dual	Hexakis tesseractic tegum
Conjugate	None
Abstract & topological properties
Flag count	15360
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B4×A1, order 768
Convex	Yes
Nature	Tame

The truncated hexadecachoric prism or thexip is a prismatic uniform polyteron that consists of 2 truncated hexadecachora, 8 octahedral prisms, and 16 truncated tetrahedral prisms. 1 truncated hexadecachoron, 1 octahedral prism, and 4 truncated tetrahedral prisms join at each vertex. As the name suggests, it is a prism based on the truncated hexadecachoron, which also makes it a convex segmentoteron.

Vertex coordinates

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

• $\left({\sqrt {2}},\,\pm {\frac {\sqrt {2}}{2}},\,0,\,0,\,\pm {\frac {1}{2}}\right).$

External links

• Klitzing, Richard. "Thexip".