Dissection of a Rhombic Triacontahedron, Golden Ratio

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Dissection of a Rhombic Triacontahedron The world of polyhedra is full of mesmerizing beauty! Starting with a golden rhombus, whose long and short diagonals have the perfect golden ratio φ = (sqrt(5)+1)/2 = 1.618 … , we can create 1/30 of a rhombic triancontahedron by extruding at a precise taper angle of -18°. This results in a shape with 30 elegant rhombic faces, showcasing the same intricate structure as the 30-piece lamp shade (refer to figure). Given the remarkable structural symmetry, we can easily mirror it around in a 5-3-5 pattern to achieve a complete triancontahedron. While observing this pattern, one might pause at half of it and ponder over its unique characteristics. The other half is not a duplicate; instead, it serves as a mirrored reflection of the first half. Therefore, both part A and part B are necessary to form a whole shape. Alternatively, you can simply mirror part A to obtain part B. If desired, try printing 30 individual pieces of the 1/30 section and assemble them together. While it's technically possible to print the entire triancontahedron, I believe the halves are far more captivating! Three different versions are included here, featuring "fair" and "loose" tolerances. Begin with the loose version first and exercise caution when handling the sharp points. When attempting to disassemble the shape, you may encounter a slight sense of discomfort due to our natural affinity for symmetry. Be mindful of where your fingers are positioned, as it's likely that you'll be grasping the same piece. Otherwise, have fun exploring this fascinating polyhedron! References https://en.wikipedia.org/wiki/Rhombic_triacontahedron http://mathworld.wolfram.com/RhombicTriacontahedron.html