Small rhombihexacron

Small rhombihexacron
(3D model) (OFF file)
Rank	3
Type	Uniform dual
Space	Spherical
Elements
Faces	24 bowties
Edges	24+24
Vertices	12+6
Vertex figures	12 squares
	6 octagons
Measures (edge length 1)
Inradius	$\frac{\sqrt{34(7+4\sqrt2)}}{17} ≈ 1.22026$
Dihedral angle	$\arccos\left(-\frac{7+4\sqrt2}{17}\right) ≈ 138.11796^\circ$
Central density	odd
Number of external pieces	48
Related polytopes
Dual	Small rhombihexahedron
Conjugate	Great rhombihexacron
Abstract & topological properties
Flag count	192
Euler characteristic	–6
Orientable	No
Properties
Symmetry	B3, order 48
Convex	No
Nature	Tame

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 $\sqrt{2\left(2+\sqrt2\right)} ≈ 2.61313$, and the long edges will be $2\sqrt{2+\sqrt2} ≈ 3.69552$. ​The bowties have two interior angles of $\arccos\left(\frac14+\frac{\sqrt2}{2}\right) ≈ 16.84212^\circ$, and two of $\arccos\left(-\frac12+\frac{\sqrt2}{4}\right) ≈ 98.42106^\circ$. The intersection has an angle of $\arccos\left(\frac14+\frac{\sqrt2}{8}\right) ≈ 64.73683^\circ$.

Vertex coordinates

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

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

External links

• Wikipedia Contributors. "Small rhombihexacron".
• McCooey, David. "Small Rhombihexacron"