# Snubahedron

Snubahedron Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymSnu
Elements
Components6 tetrahedra
Faces24 triangles
Edges12+24
Vertices24
Vertex figureEquilateral triangle, edge length 1
Measures (edge length 1)
Circumradius$\frac{\sqrt6}{4} \approx 0.61237$ Inradius$\frac{\sqrt6}{12} \approx 0.20412$ Volume$\frac{\sqrt2}{2} \approx 0.70711$ Dihedral angle$\arccos\left(\frac13\right) \approx 70.52878^\circ$ Central density6
Number of external pieces120
Level of complexity20
Related polytopes
ArmySemi-uniform Toe, edge lengths $\frac12$ (squares), $\frac{\sqrt2-1}{2}$ (between ditrigons)
RegimentSnu
DualSnubahedron
ConjugateSnubahedron
Convex coreTetrakis hexahedron
Abstract & topological properties
Flag count144
Schläfli type{3,3}
OrientableYes
Properties
SymmetryB3, order 48
ConvexNo
NatureTame

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

This is a special case of the more general small snubahedron, with double symmetry. It can be formed from the rhombihexahedron by replacing each of the cubes with the inscribed stella octangula.

Its quotient prismatic equivalent is the tetrahedral hexateroorthowedge, which is eight-dimensional.

## Vertex coordinates

The vertices of a small snubahedron of edge length 1 are given by all permutations of:

• $\left(\pm\frac{\sqrt2}{4},\,\pm\frac12,\,0\right).$ 