Hex Rosa
Inhaltsverzeichnis
Reference
Markus Rissanen: Hex Rosa. In: Bridges 2016, Pages 209–216.
DOI
Abstract
This paper describes a system of rhombic tilings with n-fold rotational symmetry for all n ! 3. A preference is given to the presentation of odd values. In addition to one centre of global rotational symmetry this system contains infinitely many relatively small evenly distributed circular patches with their own centres of n-fold local rotational symmetry. This system uses specific hexagonal modules and certain properties of them are also described.
Extended Abstract
Bibtex
@inproceedings{bridges2016:209,
author = {Markus Rissanen},
title = {Hex Rosa},
pages = {209--216},
booktitle = {Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture},
year = {2016},
editor = {Eve Torrence, Bruce Torrence, Carlo S\'equin, Douglas McKenna, Krist\'of Fenyvesi and Reza Sarhangi},
isbn = {978-1-938664-19-9},
issn = {1099-6702},
publisher = {Tessellations Publishing},
address = {Phoenix, Arizona},
url = {http://de.evo-art.org/index.php?title=Hex_Rosa},
note = {Available online at \url{http://archive.bridgesmathart.org/2016/bridges2016-209.html}}
}
Used References
[1] Gardner, M.: Extraordinary nonperiodic tiling that enriches the theory of tiles. Scientific American 236, pp. 110–121 (1977).
[2] Grünbaum and Shephard: Tilings and Patterns, W. H. Freeman, New York (1987), pp. 519–548.
[3] Alan H. Schoen at http://schoengeometry.com/b-fintil.html (read 2016-04-14).
[4] Chilton, B. L. and Coxeter, H. S. M.: Polar Zonohedra, Amer. Math. Monthly 70, pp. 946-951 (1963).
[5] Whittaker, E. J. and Whittaker, R. M.: Some Generalized Penrose Patterns from Projections of n- Dimensional Lattices, Acta Crystallographica, Vol. A44, Part 2, pp. 105–112 (1988).
[6] Kari, J. and Rissanen, M.: Sub Rosa, a System of Quasiperiodic Rhombic Substitution Tilings with n- Fold Rotational Symmetry, published first online 2016-04-04 in the Discrete & Computational Geometry at http://link.springer.com/article/10.1007/s00454-016-9779-1, a free pre-review version is available at http://arxiv.org/abs/1512.01402 (since 2015-12-04).
Links
Full Text
http://archive.bridgesmathart.org/2016/bridges2016-209.pdf
