Great hexacronic icositetrahedron explained

In geometry, the great hexacronic icositetrahedron is the dual of the great cubicuboctahedron. Its faces are kites. Part of each kite lies inside the solid, hence is invisible in solid models.

Proportions

The kites have two angles of

\arccos(	1	-
	4

	1
	2

\sqrt{2}) ≈ 117.20057038016^\circ

, one of

\arccos(-	1	+
	4

	1
	8

\sqrt{2}) ≈ 94.19914442976^\circ

and one of

\arccos(	1	+
	2

	1
	4

\sqrt{2}) ≈ 31.39971480992^\circ

. The dihedral angle equals

\arccos(	-7+4\sqrt{2

})\approx 94.531\,580\,798\,20^. The ratio between the lengths of the long and short edges is

2+	1
	2

\sqrt{2} ≈ 2.70710678118655