# Quasitruncated hexahedral prism

Quasitruncated hexahedral prism
Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymQuithip
Coxeter diagramx x4/3x3o ()
Elements
Cells8 triangular prisms, 6 octagrammic prisms, 2 quasitruncated hexahedra
Faces16 triangles, 12+24 squares, 12 octagrams
Edges24+24+48
Vertices48
Vertex figureSphenoid, edge lengths 1, 2–2, 2–2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{2-\sqrt2} ≈ 0.76537}$
Hypervolume${\displaystyle 7\frac{3-2\sqrt2}{3} ≈ 0.40034}$
Dichoral anglesStop–4–stop: 90°
Quith–8/3–stop: 90°
Quith–3–trip: 90°
Trip–4–stop: ${\displaystyle \arccos\left(\frac{\sqrt3}{3}\right) ≈ 54.73561^\circ}$
Height1
Central density7
Number of pieces56
Related polytopes
ArmySemi-uniform Sircope
RegimentQuithip
DualGreat triakis octahedral tegum
ConjugateTruncated cubic prism
Abstract properties
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryB3×A1, order 96
ConvexNo
NatureTame
Discovered by{{{discoverer}}}

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.

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:

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