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Symmetry Group of a Buckyball Torus

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Find the symmetries of an origami buckyball torus using the Orbit-Stabilizer Theorem.
The torus has 96 vertices, 24 heptagon faces, 48 hexagon faces, 24 pentagon faces.
The torus is made from 288 pentagon-hexagon-zig-zag units (PHiZZ units)

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In this solution, we compute the symmetry group of a buckyball torus.

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The symmetry group G of the torus has three generators, a 30-degree counterclockwise rotation a about the central axis, a reflection b about the plane ...

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