# Symmetry Group of a Buckyball Torus

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)

https://brainmass.com/math/geometric-shapes/symmetry-group-buckyball-torus-460783

#### Solution Preview

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 ...

#### Solution Summary

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

$2.19