# Quasitruncated hexahedral prism

Quasitruncated hexahedral prism
Rank4
TypeUniform
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${\displaystyle {\sqrt {2-{\sqrt {2}}}}\approx 0.76537}$
Hypervolume${\displaystyle 7{\frac {3-2{\sqrt {2}}}{3}}\approx 0.40034}$
Dichoral anglesStop–4–stop: 90°
Quith–8/3–stop: 90°
Quith–3–trip: 90°
Trip–4–stop: ${\displaystyle \arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }}$
Height1
Central density7
Number of external pieces56
Related polytopes
ArmySemi-uniform Sircope, edge lengths ${\displaystyle {\sqrt {2}}-1}$ (base), 1 (sides)
RegimentQuithip
DualGreat triakis octahedral tegum
ConjugateTruncated cubic prism
Abstract & topological properties
Flag count1152
Euler characteristic0
OrientableYes
Properties
SymmetryB3×A1, order 96
ConvexNo
NatureTame

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:

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