Bilinski dodecahedron

In geometry, the Bilinski dodecahedron is a convex polyhedron with twelve congruent golden rhombus faces.

[4] Bilinski's discovery corrected a 75-year-old omission in Evgraf Fedorov's classification of convex polyhedra with congruent rhombic faces.

[5] The Bilinski dodecahedron is formed by gluing together twelve congruent golden rhombi.

But due to the reversal, its non-apical vertices form two squares (red and green) and one rectangle (blue), and its fourteen vertices in all are of four different kinds: The supplementary internal angles of a golden rhombus are:[6] The faces of the Bilinski dodecahedron are twelve congruent golden rhombi; but due to the reversal, they are of three different kinds: (See also the figure with edges and front faces colored.)

[4][5] Thus removing a zone of six faces from the Bilinski dodecahedron produces a golden rhombohedron.

[8] The vertices of the zonohedra with golden rhombic faces can be computed by linear combinations of two to six generating edge vectors with coefficients 0 or 1.

3D model of a Bilinski dodecahedron
Edges and front faces colored by their symmetry positions
A Bilinski dodecahedron is a zonohedron ; it has four sets of six parallel edges. Contracting any set of six parallel edges to zero length produces a golden rhombohedron .