Quasitruncated hexahedral prism

The quasitruncated hexahedral prism or quithip, is a prismatic uniform polychoron that consists of 2 quasitruncated hexahedra, 6 octagrammic prisms, and 8 triangular prisms. Each vertex joins 1 quasitruncated hexahedron, 1 octagrammic prism, and 2 triangular prisms. As the name suggests, it is a prism based on the quasitruncated hexahedron.

Quasitruncated hexahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Quithip
Coxeter diagram	x x4/3x3o ()
Elements
Cells	8 triangular prisms, 6 octagrammic prisms, 2 quasitruncated hexahedra
Faces	16 triangles, 12+24 squares, 12 octagrams
Edges	24+24+48
Vertices	48
Vertex figure	Sphenoid, edge lengths 1, √2–√2, √2–√2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\sqrt{2-\sqrt2} ≈ 0.76537$
Hypervolume	$7\frac{3-2\sqrt2}{3} ≈ 0.40034$
Dichoral angles	Stop–4–stop: 90°
	Quith–8/3–stop: 90°
	Quith–3–trip: 90°
	Trip–4–stop: $\arccos\left(\frac{\sqrt3}{3}\right) ≈ 54.73561^\circ$
Height	1
Central density	7
Number of external pieces	56
Related polytopes
Army	Semi-uniform Sircope
Regiment	Quithip
Dual	Great triakis octahedral tegum
Conjugate	Truncated cubic prism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B3×A1, order 96
Convex	No
Nature	Tame

The quasitruncated hexahedral prism can be vertex-inscribed into the sphenoverted tesseractitesseractihexadecachoron and the great distetracontoctachoron.

Vertex coordinates

The vertices of a quasitruncated hexahedral prism of edge length 1 are given by all permutations of the first three coordinates of:

• $\left(±\frac{\sqrt2-1}{2},\,±\frac{\sqrt2-1}{2},\,±\frac12,\,±\frac12\right).$

External links

• Bowers, Jonathan. "Category 19: Prisms" (#905).

• Klitzing, Richard. "quithip".