From Colorings to Weavings

• Authors: E. Miro , A. Garciano , A. Zambrano
• Languages of publication: EN

Abstracts

EN

We present a methodology for constructing weavings from 2-colorings of the plane. In particular, we consider tilings T of the plane by triangles and their corresponding triangle groups G. We derive 2-colorings of T using the index 2 subgroups of G.

Keywords

EN

02.20.-a; 61.50.Ah; 89.75.Kd

Discipline

• 89.75.Kd: Patterns
• 61.50.Ah: Theory of crystal structure, crystal symmetry; calculations and modeling
• 02.20.-a: Group theory(for algebraic methods in quantum mechanics, see 03.65.Fd; for symmetries in elementary particle physics, see 11.30.-j)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2014
• Volume: 126
• Issue: 2
• Pages: 560-563

Dates

published

2014-08

Contributors

author

E. Miro

• Fakultät für Mathematik, Universität Bielefeld, 33615 Bielefeld, Germany
• Department of Mathematics, Ateneo de Manila University, Loyola Heights, 1108 Quezon City, Philippines

author

A. Garciano

• Department of Mathematics, Ateneo de Manila University, Loyola Heights, 1108 Quezon City, Philippines

author

A. Zambrano

• Department of Mathematics, Ateneo de Manila University, Loyola Heights, 1108 Quezon City, Philippines

References

• [1] S.J. Ramsden, V. Robins, S.T. Hyde, Acta Crystallogr. A 65, 81 (2009), doi: 10.1107/S0108767308040592
• [2] E.D.B Provido, M.L.A.N. De Las Peñas, R. Felix, Acta Crystallogr. A 69, 445 (2013), doi: 10.1107/S010876731301283X
• [3] M.L.A.N. De Las Peñas, R. Felix, E.D.B. Provido, Z. Kristallogr. 222, 443 (2007), doi: 10.1524/zkri.2007.222.9.443
• [4] D.H. Huson, Geometr. Dedic. 47, 269 (1993), doi: 10.1007/BF01263661
• [5] S.J. Ramsden, V. Robins, S.T. Hyde, S. Hungerford, EPINET: Euclidean Patterns in Non-Euclidean Tilings, The Australian National University, Canberra 2005-2009 http://epinet.anu.edu.au
• [6] J. Pach, R. Pollack, E. Welzl, Algorithmica 9, 561 (1993), doi: 10.1007/BF01190155

Identifiers

DOI

10.12693/APhysPolA.126.560