Abstract
A concept of folding for compact connected surfaces, involving the partition of the surface into combinatorially identical n-sided topological polygons, is defined. The existence of such foldings for given n and given surfaces is explored, with definitive results for the sphere and the torus. We obtain necessary conditions for the existence of such foldings in all other cases.
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Supported by Kuwait University Grant SM 043.
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Farran, H.R., El Kholy, E. & Robertson, S.A. Folding a surface to a polygon. Geom Dedicata 63, 255–266 (1996). https://doi.org/10.1007/BF00181416
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DOI: https://doi.org/10.1007/BF00181416