Rhombic triacontahedron

It can be made from a truncated octahedron by dividing the hexagonal faces into three rhombi: Let φ be the golden ratio.

If the edge length of a rhombic triacontahedron is a, surface area, volume, the radius of an inscribed sphere (tangent to each of the rhombic triacontahedron's faces) and midradius, which touches the middle of each edge are:[1] where φ is the golden ratio.

This polyhedron is a part of a sequence of rhombic polyhedra and tilings with [n, 3] Coxeter group symmetry.

Woodworker Jane Kostick builds boxes in the shape of a rhombic triacontahedron.

[6] The simple construction is based on the less than obvious relationship between the rhombic triacontahedron and the cube.

Roger von Oech's "Ball of Whacks" comes in the shape of a rhombic triacontahedron.

3D model of a rhombic triacontahedron
This animation shows a transformation from a cube to a rhombic triacontahedron by dividing the square faces into 4 squares and splitting middle edges into new rhombic faces.
A topological rhombic triacontahedron in truncated octahedron
Rhombic hexecontahedron
An example of stellations of the rhombic triacontahedron.
An example of the use of a rhombic triacontahedron in the design of a lamp
STL model of a rhombic triacontahedral box made of six panels around a cubic hole – zoom into the model to see the hole from the inside