Rhombic Dodecahedron Mirror Box
The rhombic dodecahedron is a twelve-sided solid. Each of its sides are identical equilateral diamond shapes (rhombs). The ratio of the diagonals of the sides are 1/√2. The sides are in the angle (dihedral angle) 120°. Consequently it has many unique properties. One is that copies of it can be arranged face to face to fill space without any gaps. Importantly, it is one of a few geometric solids, like the cube, that are also space fillers.
As a result of this unique property, viewing the inside of the mirror box is identical to viewing a lattice of rhombic dodecahedra from the inside.
The material is red oak with mirror glass and a transparent glass window. Since the dihedral angle is 120°, cutting the 60° angle for the wooden shell was straightforward. The facial angles were a little more challenging with the acute one at 70.53° and the obtuse angle of 109.47°.
Random view one. I wish I could have a better picture of the interior. Sorry.
Random view two.