# Small rhombihexacron

Small rhombihexacron
Rank3
TypeUniform dual
SpaceSpherical
Elements
Faces24 bowties
Edges24+24
Vertices12+6
Vertex figures12 squares
6 octagons
Measures (edge length 1)
Inradius${\displaystyle \frac{\sqrt{34(7+4\sqrt2)}}{17} ≈ 1.22026}$
Dihedral angle${\displaystyle \arccos\left(-\frac{7+4\sqrt2}{17}\right) ≈ 138.11796^\circ}$
Central densityodd
Number of external pieces48
Related polytopes
DualSmall rhombihexahedron
ConjugateGreat rhombihexacron
Abstract & topological properties
Flag count192
Euler characteristic–6
OrientableNo
Properties
SymmetryB3, order 48
ConvexNo
NatureTame

The small rhombihexacron is a uniform dual polyhedron. It consists of 24 bowties.

It appears the same as the small hexacronic icositetrahedron.

If its dual, the small rhombihexahedron, has an edge length of 1, then the short edges of the bowties will measure ${\displaystyle \sqrt{2\left(2+\sqrt2\right)} ≈ 2.61313}$, and the long edges will be ${\displaystyle 2\sqrt{2+\sqrt2} ≈ 3.69552}$. ​The bowties have two interior angles of ${\displaystyle \arccos\left(\frac14+\frac{\sqrt2}{2}\right) ≈ 16.84212^\circ}$, and two of ${\displaystyle \arccos\left(-\frac12+\frac{\sqrt2}{4}\right) ≈ 98.42106^\circ}$. The intersection has an angle of ${\displaystyle \arccos\left(\frac14+\frac{\sqrt2}{8}\right) ≈ 64.73683^\circ}$.

## Vertex coordinates

A small rhombihexacron with dual edge length 1 has vertex coordinates given by all permutations of:

• ${\displaystyle \left(±\left(2+\sqrt2\right),\,0,\,0\right),}$
• ${\displaystyle \left(±1,\,±1,\,0\right).}$