Abstract
Summary We enumerate all Hamilton circuits on the dual graph of the dodecahedron, group them according to symmetry, and then discuss which of them may be realized as snake patterns on the Megaminx puzzle. We find that there are eleven shapes that may be obtained without taking the puzzle apart (legal shapes) and ten more that can be achieved if you swap two pieces (illegal). With color taken into account, there are 700 ways to put a snake on the Megaminx, 280 of them legal. Supplemental data for this article is available online at http://dx.doi.org/10.1080/0025570X.2022.2001286
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