Small rhombihexacron explained

In geometry, the small rhombihexacron (or small dipteral disdodecahedron) is the dual of the small rhombihexahedron. It is visually identical to the small hexacronic icositetrahedron. Its faces are antiparallelograms formed by pairs of coplanar triangles.

Proportions

Each antiparallelogram has two angles of

\arccos(	1	+
	4

	1
	2

\sqrt{2}) ≈ 16.84211623630^\circ

and two angles of

\arccos(-	1	+
	2

	1
	4

\sqrt{2}) ≈ 98.42105811815^\circ

. The diagonals of each antiparallelogram intersect at an angle of

\arccos(	1	+
	4

	1
	8

\sqrt{2}) ≈ 64.73682564555^\circ

. The dihedral angle equals

\arccos(	-7-4\sqrt{2

})\approx 138.117\,959\,055\,51^. The ratio between the lengths of the long edges and the short ones equals

\sqrt{2}