Articolul precedent |
Articolul urmator |
210 0 |
SM ISO690:2012 ZAMORZAEVA-ORLEANSCHI, Elizaveta. On 3-isohedral tilings of sphere for group series n ×. In: Conference on Applied and Industrial Mathematics: CAIM 2018, 20-22 septembrie 2018, Iași, România. Chișinău, Republica Moldova: Casa Editorial-Poligrafică „Bons Offices”, 2018, Ediţia a 26-a, p. 111. ISBN 978-9975-76-247-2. |
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Conference on Applied and Industrial Mathematics Ediţia a 26-a, 2018 |
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Conferința "Conference on Applied and Industrial Mathematics" Iași, România, Romania, 20-22 septembrie 2018 | ||||||
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Pag. 111-111 | ||||||
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A tiling W of the sphere with disks is called k-isohedral with respect to a discrete isometry group G if G maps the tiling W onto itself and the disks of W fall into k transitivity classes under the action of the group G. Two pairs (W;G) and (W0;G0) belong to the same Delone class if there exists a homeomorphic transformation ' of the sphere such that ' maps the tiling W onto the tiling W0 and the relation G = 'φ-1G0' holds. Some methods were developed that make it possible to obtain (k + 1)-isohedral tilings with disks if the respective k-isohedral tilings with disks are known. In [1] the splitting procedure was applied to isohedral tilings of the sphere with disks resulting in all the fundamental Delone classes of 2-isohedral tilings of the sphere with disks for all 7 in nite series and 7 sporadic discrete isometry groups of the sphere. The splitting procedure has already been applied to 2-isohedral tilings of the sphere with disks for group series nn, nn, 22n, and n. Now turning to the series n of isometry groups (which corresponds to the series f2N of 3dimensional point groups of isometries) we restrict ourselves to 3-isohedral tilings with disks that have at least 3 vertices, so digonal disks are excluded. Thus the splitting procedure has been applied to all the 20 series of Delone classes of fundamental 2-isohedral tilings of the sphere with disks. As a result we have obtained 105 series of Delone classes of fundamental 3-isohedral tilings of the sphere with disks that have at least 3 vertices, among them 94 series of Delone classes are normal in terminology of Grunbaum and Shephard. |
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