On the complete enumeration of 3-isohedral spherical tilings for group series n£
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2021-07-09 15:52
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ZAMORZAEVA-ORLEANSCHI, Elizaveta. On the complete enumeration of 3-isohedral spherical tilings for group series n£. In: Mathematics and Information Technologies: Research and Education, Ed. 2021, 1-3 iulie 2021, Chişinău. Chișinău, Republica Moldova: 2021, p. 88.
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Mathematics and Information Technologies: Research and Education 2021
Conferința "Mathematics and Information Technologies: Research and Education"
2021, Chişinău, Moldova, 1-3 iulie 2021

On the complete enumeration of 3-isohedral spherical tilings for group series n£


Pag. 88-88

Zamorzaeva-Orleanschi Elizaveta
 
Vladimir Andrunachievici Institute of Mathematics and Computer Science
 
 
Disponibil în IBN: 1 iulie 2021


Rezumat

As is known there are 7 infinite series and 7 sporadic discrete isometry groups of the sphere. In [1] we obtained all the fundamental Delone classes of 2-isohedral tilings of the sphere with disks, i.e. tilings with 2 transitivity classes of disks. Some splitting procedure applied to fundamental 2-isohedral tilings yields fundamental 3-isohedral tilings. All the fundamental 3-isohedral tilings have already been obtained for group series ¤nn, nn, ¤22n, and n¤. Now we turn to the series n£ of isometry groups of the sphere, which corresponds to the series f2N of 3-dimensional point groups of isometries. Earlier we obtained so-called proper 3-isohedral tilings of the sphere by disks with at least 3 vertices. Applying the splitting procedure to all the 20 series of Delone classes of fundamental 2-isohedral tilings of the sphere with disks, gives 293 series of Delone classes of fundamental 3-isohedral tilings of the sphere with disks. The results coincide with the numerical results of [2], where the author developed some algorithms based on the theory of Delaney–Dress symbols and implemented algorithms using computer.