Abstract
By Steinitz' Theorem all triangulations of a sphere are generated from one triangulation with four vertices by certain sequences of operations called vertex splittings. A theorem of Barnette asserts that all triangulations of the projective plane can be generated from two irreducible triangulations. In the present work we obtain an analogous result for the torus: we show that all triangulations of the torus are generated by 21 irreducible triangulations (they are found explicitly) by applying the same vertex splitting operations. Two tables, one figure.
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Additional information
Translated from Ukrainskií Geometricheskií Sbornik, No. 30, 1987, pp. 52–62.
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Lavrenchenko, S.A. Irreducible triangulations of the torus. J Math Sci 51, 2537–2543 (1990). https://doi.org/10.1007/BF01104169
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DOI: https://doi.org/10.1007/BF01104169