These two polyhedra are known as “Golden Rhombohedra” because the diagonals of the faces are the golden ratio. They combine and tile 3D space in ways that are complex and beautiful.
These files have inserts for magnets to make is easier to visualize and understand how they fit together.
These two polyhedra are part of a family of polyhedra known as the “golden isozonohedra.” There are only five golden isozonohedra. The “acute golden rhombohedron” and “obtuse golden rhombohedron” provide here are the most simple, but they can be combined together to form three more golden isozonohedra, the “Bilinski dodecahedron”, the “rhombic icosahedron,” and the “rhombic triacontahedron.”
See here for video of finished pieces and demonstration on how they fit together: https://youtu.be/AQKMeJGCrfE
The files provided are for one version of the acute golden rhombohedron and two versions of the obtuse golden rhombohedron. Files are provided with or without supports.
The two versions of the obtuse golden rhombohedron are the same shape, but one has magnet holes on all faces, while the other has magnet holes on only half of the faces. Most of the obtuse golden rhombohedra end up on the outside of the final polyhedra and so don’t need magnets on the outside faces. This also helps cut costs in terms of number of magnets needed. Obtuse golden rhombohedra that are contained entirely within the larger polyhedra need to have magnets on all faces, but you’ll only need three of these.
To make all the five golden isozonohedra you will need: 10 acute golden rhombohedra 7 obtuse golden rhombohedra with magnets on three faces 3 obtuse golden rhombohedra with magnets on all faces
The magnet holes fit 1/8” by 1/16” cylindrical magnets. The polarity of magnets on each face must be facing opposite directions, and the pattern must be consistent on every face of every piece in order for all of the faces to snap together interchangeably. Magnets can be press fit with pliers, no glue needed.
The magnets used in the design and assembly of this model were purchased through www.kjmagnetics.com.