geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

, the medial deltoidal hexecontahedron is a nonconvex

isohedral In geometry, a tessellation of dimension (a plane tiling) or higher, or a polytope of dimension (a polyhedron) or higher, is isohedral or face-transitive if all its faces are the same. More specifically, all faces must be not merely congruen ...

polyhedron In geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional figure with flat polygonal Face (geometry), faces, straight Edge (geometry), edges and sharp corners or Vertex (geometry), vertices. The term "polyhedron" may refer ...

. 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 number, a nu ...

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 construc ...

. Its 60 intersecting

quadrilateral In Euclidean geometry, geometry a quadrilateral is a four-sided polygon, having four Edge (geometry), edges (sides) and four Vertex (geometry), corners (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''l ...

faces are

kites A kite is a tethered heavier than air flight, heavier-than-air craft with wing surfaces that react against the air to create Lift (force), lift and Drag (physics), drag forces. A kite consists of wings, tethers and anchors. Kites often have ...

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