In geometry, the medial deltoidal hexecontahedron is a nonconvex isohedral polyhedron. It is the

dual Dual or Duals may refer to: Paired/two things * Dual (mathematics), a notion of paired concepts that mirror one another ** Dual (category theory), a formalization of mathematical duality *** see more cases in :Duality theories * Dual (grammatical ...

of the

rhombidodecadodecahedron In geometry, the rhombidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U38. It has 54 faces (30 squares, 12 pentagons and 12 pentagrams), 120 edges and 60 vertices. It is given a Schläfli symbol t0,2, and by the Wythoff const ...

. Its 60 intersecting quadrilateral faces are kites.

Proportions

The kites have two angles of

\arccos(\frac)\approx 80.405\,931\,773\,14^

, one of

\arccos(-\frac+\frac\sqrt)\approx 58.184\,446\,117\,59^

and one of

\arccos(-\frac-\frac\sqrt)\approx 141.003\,690\,336\,13^

. The dihedral angle equals

\arccos(-\frac)\approx 135.584\,691\,402\,81^

. The ratio between the lengths of the long and short edges is

\frac\approx 1.938\,748\,901\,931\,75

. Part of each kite lies inside the solid, hence is invisible in solid models.

References

External links

*
Uniform polyhedra and duals
Dual uniform polyhedra {{polyhedron-stub