geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, 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 congruent ...

polyhedron In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all on th ...

. 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

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

truncated dodecadodecahedron In geometry, the truncated dodecadodecahedron (or stellatruncated dodecadodecahedron) is a nonconvex uniform polyhedron, indexed as U59. It is given a Schläfli symbol t0,1,2. It has 54 faces (30 squares, 12 decagons, and 12 decagrams), 180 edges ...

. 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 A dihedral angle is the angle between two intersecting planes or half-planes. In chemistry, it is the clockwise angle between half-planes through two sets of three atoms, having two atoms in common. In solid geometry, it is defined as the uni ...

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