Rhombicosacron Explained

In geometry, the rhombicosacron (or midly dipteral ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform rhombicosahedron, U56. It has 50 vertices, 120 edges, and 60 crossed-quadrilateral faces.

Proportions

Each face has two angles of

\arccos(	3
	4

) ≈ 41.40962210927^\circ

and two angles of

\arccos(-	1
	6

) ≈ 99.59406822686^\circ

. The diagonals of each antiparallelogram intersect at an angle of

\arccos(	1	+
	8

	7\sqrt{5

})\approx 38.996\,309\,663\,87^. The dihedral angle equals

\arccos(-	5
	7

) ≈ 135.58469140281^\circ

. The ratio between the lengths of the long edges and the short ones equals

	3	+
	2

	1
	2

\sqrt{5}

, which is the square of the golden ratio.