# Truncated stella octangula

Truncated stella octangula
Rank3
TypeUniform
Notation
Bowers style acronymTisso
Coxeter diagram (β4o3x)
Elements
Components2 truncated tetrahedra
Faces
Edges12+24
Vertices24
Vertex figureIsosceles triangle, edge lengths 1. 3, 3
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {22}}{4}}\approx 1.17260}$
Volume${\displaystyle {\frac {23{\sqrt {2}}}{6}}\approx 5.42115}$
Dihedral angles3–6: ${\displaystyle \arccos \left(-{\frac {1}{3}}\right)\approx 109.47122^{\circ }}$
6–6: ${\displaystyle \arccos \left({\frac {1}{3}}\right)\approx 70.52878^{\circ }}$
Central density2
Number of external pieces32
Level of complexity5
Related polytopes
ArmySemi-uniform sirco, edge lengths ${\displaystyle {\frac {\sqrt {2}}{2}}}$ (squares), 1 (triangles)
RegimentTisso
DualTriakis stella octangula
ConjugateNone
Convex coreOctahedron
Abstract & topological properties
Flag count144
OrientableYes
Properties
SymmetryB3, order 48
Flag orbits3
ConvexNo
NatureTame

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.

## Vertex coordinates

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

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