# Small snubahedron

Small snubahedron
Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymSis
Elements
Components6 tetrahedra
Faces24 triangles
Edges12+24
Vertices24
Vertex figureEquilateral triangle, edge length 1
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt6}{4} ≈ 0.61237}$
Inradius${\displaystyle \frac{\sqrt6}{12} ≈ 0.20412}$
Volume${\displaystyle \frac{\sqrt2}{2} ≈ 0.70711}$
Dihedral angle${\displaystyle \arccos\left(\frac13\right) ≈ 70.52878^\circ}$
Central density6
Related polytopes
ArmySemi-uniform Toe
RegimentSis
DualSmall snubahedron
ConjugateSmall snubahedron
Abstract & topological properties
Schläfli type{3,3}
OrientableYes
Properties
SymmetryA3, order 24
ConvexNo
NatureTame

The small snubahedron, sis, or compound of six tetrahedra with rotational freedom is a uniform polyhedron compound. It consists of 24 triangles, with three faces joining at a vertex.

This compound has rotational freedom, represented by an angle θ. At θ = 0°, all six tetrahedra coincide. We rotate these tetrahedra around their 2-fold axes of symmetry (2 each), seeing them as digonal antiprisms. At θ = 45° the compound has double symmetry resulting in the snubahedron.

This compound can be formed by taking one of the tetrahedra inscribed in each cube of the rhombisnub dishexahedron.

## Vertex coordinates

The vertices of a small snubahedron of edge length 1 and rotation angle θ are given by all even permutations of:

• ${\displaystyle \left(±\frac{\cos(\theta)+\sin(\theta)}{2\sqrt2},\,±\frac{\cos(\theta)-\sin(\theta)}{2\sqrt2},\,±\frac{\sqrt2}{4}\right).}$