A “regular” pentagonal tiling of the plane
نویسندگان
چکیده
منابع مشابه
A “regular” Pentagonal Tiling of the Plane
The paper introduces conformal tilings, wherein tiles have specified conformal shapes. The principal example involves conformally regular pentagons which tile the plane in a pattern generated by a subdivision rule. Combinatorial symmetries imply rigid conformal symmetries, which in turn illustrate a new type of tiling self-similarity. In parallel with the conformal tilings, the paper develops d...
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In this paper, we study the number of tilings of the hyperbolic plane that can be constructed, starting from a single pentagonal tile, the only permitted transformations on the basic tile being the replication by displacement along the lines of the pentagrid. We obtain that there is no such tiling with five colours, that there are exactly two of them with four colours and a single trivial tilin...
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We present scanning tunnelling microscopy studies and first principles calculation on the 2D crystallization of pentagonal pentamethylcorannulene on a Cu(111) surface under ultrahigh vacuum in the temperature range of 50 K to 400 K. The observed 2D crystal phases and their packing densities are compared to tiling options of hard pentagons. Temperature change-induced reversible phase transitions...
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ژورنال
عنوان ژورنال: Conformal Geometry and Dynamics of the American Mathematical Society
سال: 1997
ISSN: 1088-4173
DOI: 10.1090/s1088-4173-97-00014-3