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Coordination sequences for hyperbolic tilings
Published/Copyright:
July 28, 2010
Abstract
Coordination sequences have been determined for tilings {p, q} of the hyperbolic plane in which q p-gons meet at each vertex. The number of vertices in successive shells is related by a recurrence to the numbers in earlier shells and grows exponentially. General expressions for the recurrences are given and numerical expressions for the growth rate are determined. For p = 3 – 10, 12, 14, 16 and 18 exact expressions, that require finding roots of polynomials of degree ≤4, are given for the coordination sequence. Some differences between hyperbolic tilings and 3-dimensional nets are noted.
Published Online: 2010-7-28
Published in Print: 1998-3-1
© 2015 Oldenbourg Wissenschaftsverlag GmbH, Rosenheimer Str. 145, 81671 München
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Articles in the same Issue
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- Preparation and crystal structure determination of triphenylmethanide cesium · 1.5 dimethoxyethane and of phenothiazine cesium diglyme
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