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- W1757560450 abstract "In [B.Gruenbaum, G.C. Shephard, Spherical tilings with transitivity properties, in: The geometric vein, Springer, New York, 1981, pp. 65-98], they proved for every spherical normal tiling by congruent tiles, if it is isohedral, then the graph is a Platonic solid, an Archimedean dual, an n-gonal bipyramid (n>2), or an n-gonal trapezohedron (i.e., the pseudo-double wheel of 2n faces). In the classification of spherical monohedral tilings, one naturally asks an inverse problem of their result: For a spherical monohedral tiling of the above mentioned topologies, when is the tiling isohedral? We prove that for any spherical monohedral quadrangular tiling being topologically a trapezohedron, if the number of faces is 6, or 8, if the tile is a kite, a dart or a rhombi, or if the tile is convex, then the tiling is isohedral." @default.
- W1757560450 created "2016-06-24" @default.
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- W1757560450 date "2013-12-10" @default.
- W1757560450 modified "2023-09-25" @default.
- W1757560450 title "Spherical tilings by congruent quadrangles over pseudo-double wheels (III) - the essential uniqueness in case of convex tiles" @default.
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- W1757560450 doi "https://doi.org/10.48550/arxiv.1312.3026" @default.
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