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 great ditrigonal dodecacronic hexecontahedron (or great lanceal trisicosahedron) 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

uniform A uniform is a variety of costume worn by members of an organization while usually participating in that organization's activity. Modern uniforms are most often worn by armed forces and paramilitary organizations such as police, emergency serv ...

great ditrigonal dodecicosidodecahedron. Its 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 ...

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

Proportions

Kite faces have two angles of

\arccos(\frac-\frac\sqrt)\approx 98.183\,872\,491\,81^

, one of

\arccos(-\frac+\frac\sqrt)\approx 112.296\,452\,073\,54^

and one of

\arccos(-\frac+\frac\sqrt)\approx 51.335\,802\,942\,83^

. Its dihedral angles equal

\arccos()\approx 127.686\,523\,427\,48^

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

\frac\approx 1.917\,288\,176\,70

References

* p. 62

External links

* Dual uniform polyhedra {{polyhedron-stub