Geodesic
On local operations that preserve symmetries and on preserving polyhedrality of maps
Ars Mathematica Contemporanea, Tome 24 (2024) no. 2, article no. 01, 32 p.

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We prove that local operations that preserve all symmetries, as e.g. dual, truncation, medial, or join, as well as local operations that are only guaranteed to preserve all orientation-preserving symmetries, as e.g. gyro or snub, preserve the polyhedrality of simple maps. This generalizes a result by Mohar proving this for the operation dual. We give the proof based on an abstract characterization of these operations, prove that the operations are well defined, and also demonstrate the close connection between these operations and Delaney-Dress symbols.
DOI : 10.26493/1855-3974.2749.b64
Keywords: Embedded graph, map, polyhedral embedding, operation, symmetry, tiling 
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Gunnar Brinkmann; Heidi Van den Camp. On local operations that preserve symmetries and on preserving polyhedrality of maps. Ars Mathematica Contemporanea, Tome 24 (2024) no. 2, article  no. 01, 32 p. doi : 10.26493/1855-3974.2749.b64. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2749.b64/

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