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 small ditrigonal dodecacronic hexecontahedron (or fat star) 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 ...

small ditrigonal dodecicosidodecahedron. It is visually identical to the small dodecicosacron. Its faces are darts. A part of each dart lies inside the solid, hence is invisible in solid models.

Proportions

Faces have two angles of

\arccos(\frac+\frac\sqrt)\approx 12.661\,078\,804\,43^

, one of

\arccos(-\frac-\frac\sqrt)\approx 116.996\,396\,851\,70^

and one of

360^-\arccos(-\frac-\frac\sqrt)\approx 217.681\,445\,539\,45^

. Its dihedral angles equal

\arccos()\approx 146.230\,659\,755\,53^

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

\frac\approx 1.110\,008\,944\,41

References

External links

* Dual uniform polyhedra {{polyhedron-stub