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Articolul urmator |
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SM ISO690:2012 ZAMORZAEVA-ORLEANSCHI, Elizaveta. On normal 3-isohedral spherical tilings for group series n×. In: Conference on Applied and Industrial Mathematics: CAIM 2022, Ed. 29, 25-27 august 2022, Chişinău. Chișinău, Republica Moldova: Casa Editorial-Poligrafică „Bons Offices”, 2022, Ediţia a 29, pp. 166-167. ISBN 978-9975-81-074-6. |
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Conference on Applied and Industrial Mathematics Ediţia a 29, 2022 |
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Conferința "Conference on Applied and Industrial Mathematics" 29, Chişinău, Moldova, 25-27 august 2022 | ||||||
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Pag. 166-167 | ||||||
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A tiling W of the sphere with disks is called 3-isohedral with respect to an isometry group G if G maps W onto itself and the tiles of W fall into exactly 3 transitivity classes under the group G. Recently we have obtained all the fundamental 3-isohedral tilings of the sphere with disks for group series n×, n = 1, 2, . . . , which comprise 293 series of Delone classes. In [1] B. Gr¨unbaum and G. C. Shephard distinguish the so-called normal tilings with the additional restriction that the intersection of any set of tiles is a connected (possibly empty) set. These intersections define edges and vertices of the tiling. One more restriction is that each edge of the tiling has two endpoints which are vertices of the tiling. We choose tilings satisfying the normality conditions among all fundamental 3-isohedral tilings of the sphere with disks for group series n×. As a result there are 92 series of Delone classes of normal fundamental 3-isohedral tilings of the sphere for group series n×. Earlier all the normal fundamental tilings of the sphere for group series ∗nn, nn, ∗22n, and n∗ were listed in [2]. |
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