Dissection of a Rhombic Triacontahedron, Golden Ratio by lgbu

Last crawled date: 3 years, 1 month ago

Dissection of a Rhombic Triacontahedron
The world of polyhedra is full of beauty! If we start with a golden rhombus, whose long and short diagonals have the golden ratio φ {= (sqrt(5)+1)/2 = 1. 618 …}, and extrude at a taper angle of -18°, we get 1/30 of a rhombic triancontahedron with 30 rhombic faces. It has the same structure as the 30-piece lamp shade (refer to figure).
In light of the structural symmetry, we can just mirror it around in a 5-3-5 pattern for a whole triancontahedron. Of course, in the process, we could observe the pattern and stop at one-half of it and think it over. The other half is not the same. Rather, it is the mirror of the first half. Therefore, you need both part A and part B to make a whole. Of course, you could just mirror part A to get a part B. If you like, you could try printing 30 pieces of the 1/30 piece and assemble them together.
Although we could print the whole triancontahedron, I think the halves are much more interesting! Three versions are included here, with “fair” and “loose” tolerances. Please try the loose version first and be careful when handling the sharp points.
Also, it feels a bit awkward when you try to pull it apart because we are so used to symmetry. Please watch where your fingers are holding on to. Most likely, you might be pulling the same piece.
Otherwise, have fun!
References
https://en.wikipedia.org/wiki/Rhombic_triacontahedron
http://mathworld.wolfram.com/RhombicTriacontahedron.html