Truncated stella octangula

Truncated stella octangula
(3D model) (OFF file)
Rank	3
Type	Uniform
Notation
Bowers style acronym	Tisso
Coxeter diagram	(β4o3x)
Elements
Components	2 truncated tetrahedra
Faces	8 triangles 8 hexagons
Edges	12+24
Vertices	24
Vertex figure	Isosceles triangle, edge lengths 1. √3, √3
Measures (edge length 1)
Circumradius	${\frac {\sqrt {22}}{4}}\approx 1.17260$
Volume	${\frac {23{\sqrt {2}}}{6}}\approx 5.42115$
Dihedral angles	3–6: $\arccos \left(-{\frac {1}{3}}\right)\approx 109.47122^{\circ }$
	6–6: $\arccos \left({\frac {1}{3}}\right)\approx 70.52878^{\circ }$
Central density	2
Number of external pieces	32
Level of complexity	5
Related polytopes
Army	Semi-uniform sirco, edge lengths ${\frac {\sqrt {2}}{2}}$ (squares), 1 (triangles)
Regiment	Tisso
Dual	Triakis stella octangula
Conjugate	None
Convex core	Octahedron
Abstract & topological properties
Flag count	144
Orientable	Yes
Properties
Symmetry	B3, order 48
Flag orbits	3
Convex	No
Nature	Tame

The truncated stella octangula, truncated stellated octahedron, tisso, or compound of two truncated tetrahedra is a uniform polyhedron compound. It consists of 8 triangles and 8 hexagons, with one triangle and two hexagons joining at each vertex. As the name suggests, it can be derived as the truncation of the stella octangula, the compound of two tetrahedra.

Its quotient prismatic equivalent is the truncated tetrahedral alterprism, which is four-dimensional.

Gallery

Vertex coordinates

The vertices of a truncated stella octangula of edge length 1 can be given by all permutations of:

• $\left(\pm {\frac {3{\sqrt {2}}}{4}},\,\pm {\frac {\sqrt {2}}{4}},\,\pm {\frac {\sqrt {2}}{4}}\right)$.

External links

• Bowers, Jonathan. "Polyhedron Category C2: Compound Truncates" (#7).

• Klitzing, Richard. "tisso".
• Wikipedia contributors. "Compound of two truncated tetrahedra".