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Hamiltonian Cycles on Archimedean Solids Are Twisting Free

Richard Ehrenborg
The American Mathematical Monthly
Vol. 121, No. 2 (February 2014), pp. 158-161
DOI: 10.4169/amer.math.monthly.121.02.158
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.121.02.158
Page Count: 4
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Hamiltonian Cycles on Archimedean Solids Are Twisting Free
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Abstract

Abstract We prove that a Hamiltonian cycle on the faces of an Archimedean solid is twisting free, that is, when returning to the first facet of the cycle, it has the same orientation as in the beginning. We also explore a continuous analogue on the unit sphere.

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