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November 2013 Classification of spherical tilings by congruent quadrangles over pseudo-double wheels (I) -- a special tiling by congruent concave quadrangles
Yohji Akama
Hiroshima Math. J. 43(3): 285-304 (November 2013). DOI: 10.32917/hmj/1389102577

Abstract

Every simple quadrangulation of the sphere is generated by a graph called a pseudo-double wheel with two local expansions (Brinkmann et al. "Generation of simple quadrangulations of the sphere.'' Discrete Math., Vol. 305, No. 1-3, pp. 33--54, 2005). So, toward a classification of the spherical tilings by congruent quadrangles, we propose to classify those with the tiles being convex and the graphs being pseudo-double wheels. In this paper, we verify that a certain series of assignments of edge-lengths to pseudo-double wheels does not admit a tiling by congruent convex quadrangles. Actually, we prove the series admits only one tiling by twelve congruent concave quadrangles such that the symmetry of the tiling has only three perpendicular 2-fold rotation axes, and the tiling seems to be new.

Citation

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Yohji Akama. "Classification of spherical tilings by congruent quadrangles over pseudo-double wheels (I) -- a special tiling by congruent concave quadrangles." Hiroshima Math. J. 43 (3) 285 - 304, November 2013. https://doi.org/10.32917/hmj/1389102577

Information

Published: November 2013
First available in Project Euclid: 7 January 2014

zbMATH: 1295.52024
MathSciNet: MR3161319
Digital Object Identifier: 10.32917/hmj/1389102577

Subjects:
Primary: 52C20
Secondary: 05B45, 05C10, 51M20

Rights: Copyright © 2013 Hiroshima University, Mathematics Program

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Vol.43 • No. 3 • November 2013
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