Quasitruncated hexahedron

Quasitruncated hexahedron
(3D model) (OFF file)
Rank	3
Type	Uniform
Notation
Bowers style acronym	Quith
Coxeter diagram	x4/3x3o ()
Elements
Faces	8 triangles, 6 octagrams
Edges	12+24
Vertices	24
Vertex figure	Isosceles triangle, edge lengths 1, √2–√2, √2–√2
Measures (edge length 1)
Circumradius	${\frac {\sqrt {7-4{\sqrt {2}}}}{2}}\approx 0.57947$
Volume	$7{\frac {3-2{\sqrt {2}}}{3}}\approx 0.40034$
Dihedral angles	8/3–8/3: 90°
	8/3–3: $\arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }$
Central density	7
Number of external pieces	54
Level of complexity	11
Related polytopes
Army	Sirco, edge length ${\sqrt {2}}-1$
Regiment	Quith
Dual	Great triakis octahedron
Conjugate	Truncated cube
Convex core	Octahedron
Abstract & topological properties
Flag count	144
Euler characteristic	2
Orientable	Yes
Genus	0
Properties
Symmetry	B3, order 120
Flag orbits	3
Convex	No
Nature	Tame

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

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

Related polyhedra

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

External links

• Bowers, Jonathan. "Polyhedron Category 2: Truncates" (#17).

• Klitzing, Richard. "quith".
• Wikipedia contributors. "Stellated truncated hexahedron".
• McCooey, David. "Stellated Truncated Hexahedron"