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 disdyakis triacontahedron 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 ...

truncated dodecadodecahedron. It has 120 triangular faces.

Proportions

The triangles have one angle of

\arccos(-\frac)\approx 95.739\,170\,477\,27^

, one of

\arccos(\frac+\frac\sqrt)\approx 8.142\,571\,179\,89^

and one of

\arccos(-\frac+\frac\sqrt)\approx 76.118\,258\,342\,85^

. The dihedral angle equals

\arccos(-\frac)\approx 144.903\,198\,772\,42^

. Part of each triangle lies within the solid, hence is invisible in solid models.

References

External links

* Dual uniform polyhedra {{polyhedron-stub