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A "Regular" Pentagonal Tiling of the Plane (1997)
| Content Provider | CiteSeerX |
|---|---|
| Author | Stephenson, Kenneth Bowers, Philip L. |
| Abstract | . 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 discrete tilings based on circle packings. These faithfully reflect the key features of the theory and provide the tiling illustrations of the paper. Moreover, it is shown that under refinement the discrete tiles converge to their true conformal shapes, shapes for which no other approximation techniques are known. The paper concludes with some further examples which may contribute to the study of tilings and shinglings being carried forward by Cannon, Floyd, and Parry. Introduction First, of course, there is no regular pentagonal tiling of the plane! That is to say, no euclidean one. However, o... |
| File Format | |
| Journal | Conformal Geom. Dynam |
| Publisher Date | 1997-01-01 |
| Access Restriction | Open |
| Subject Keyword | Conformal Tiling Discrete Tile Approximation Technique Discrete Tiling True Conformal Shape Introduction First Key Feature Combinatorial Symmetry Euclidean One Circle Packing Conformal Shape Rigid Conformal Symmetry Tiling Illustration Subdivision Rule New Type Regular Pentagonal Tiling Regular Pentagon Principal Example Wherein Tile |
| Content Type | Text |
