Tesseractihexadecachoric prism

Tesseractihexadecachoric prism
File:Tesseractihexadecachoric prism.png
Rank	5
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Tahp
Coxeter diagram	x o4x3x3o ()
Elements
Tera	16 truncated tetrahedral prisms, 8 truncated octahedral prisms, 2 tesseractihexadecachora
Cells	32 triangular prisms, 24 cubes, 64 hexagonal prisms, 32 truncated tetrahedra, 16 truncated octahedra
Faces	64 triangles, 48+96+96 squares, 128 hexagons
Edges	96+192+192
Vertices	192
Vertex figure	Digonal disphenoidal pyramid, edge lengths 1, √2, √3 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\frac{\sqrt{19}}{2} \approx 2.17945$
Hypervolume	$\frac{307}{6} \approx 51.16667$
Diteral angles	Tope–hip–tuttip: 120°
	Tuttip–trip–tuttip: 120°
	Tope–cube–tope: 90°
	Tah–toe–tope: 90°
	Tah–tut–tuttip: 90°
Height	1
Central density	1
Number of external pieces	26
Level of complexity	30
Related polytopes
Army	Tahp
Regiment	Tahp
Dual	Disphenoidal enneacontahexachoric tegum
Conjugate	None
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B4×A1, order 768
Convex	Yes
Nature	Tame

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

Vertex coordinates

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

• $\left(\pm\sqrt2,\,\pm\sqrt2,\,\pm\frac{\sqrt2}{2},\,0,\,\pm\frac12\right)$.

External links

• Klitzing, Richard. "Tahp".