# Quasitruncated hexahedron

Quasitruncated hexahedron
Rank3
TypeUniform
Notation
Bowers style acronymQuith
Coxeter diagramx4/3x3o ()
Elements
Faces8 triangles, 6 octagrams
Edges12+24
Vertices24
Vertex figureIsosceles triangle, edge lengths 1, 2–2, 2–2
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {7-4{\sqrt {2}}}}{2}}\approx 0.57947}$
Volume${\displaystyle 7{\frac {3-2{\sqrt {2}}}{3}}\approx 0.40034}$
Dihedral angles8/3–8/3: 90°
8/3–3: ${\displaystyle \arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }}$
Central density7
Number of external pieces54
Level of complexity11
Related polytopes
ArmySirco, edge length ${\displaystyle {\sqrt {2}}-1}$
RegimentQuith
DualGreat triakis octahedron
ConjugateTruncated cube
Convex coreOctahedron
Abstract & topological properties
Flag count144
Euler characteristic2
OrientableYes
Genus0
Properties
SymmetryB3, order 120
Flag orbits3
ConvexNo
NatureTame

The quasitruncated hexahedron, the quasitruncated cube, or quith, also called the stellated truncated hexahedron, is a uniform polyhedron. It consists of 8 triangles and 6 octagrams. Each vertex joins one triangle and two octagrams. As the name suggests, it can be obtained by quasitruncation of the cube.

## Vertex coordinates

A quasitruncated hexahedron of edge length 1 has vertex coordinates given by all permutations and sign changes of

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

## Related polyhedra

The quasitruncated rhombihedron is a uniform polyhedron compound composed of 5 quasitruncated hexahedra.