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The American Mathematical Monthly Volume 130, 2023 - Issue 4
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Notes

Vertex to Vertex Geodesics on Platonic Solids

Serge TroubetzkoyCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-1411-2383View further author information
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Pages 379-382 | Received 09 Feb 2022, Accepted 31 Aug 2022, Published online: 09 Feb 2023
 
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Abstract

We give a simple proof based on symmetries that there are no geodesics from a vertex to itself in the cube, tetrahedron, octahedron, and icosahedron.

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Notes on contributors

Serge Troubetzkoy

Serge E. Troubetzkoy received his B.A. from Yale University in 1982 and his Ph.D. from Stanford University in 1987. After a Brownian career path: Leningrad, Toronto, Warwick, Bielefeld, Stony Brook, and UAB, he settled down in Marseille.

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