Michael Baake et al 1997 J. Phys. A: Math. Gen. 30 3029 doi:10.1088/0305-4470/30/9/016
The torus parametrization of quasiperiodic LI-classes
Michael Baake
, Joachim Hermisson and Peter A B Pleasants
The torus parametrization of quasiperiodic local isomorphism classes is introduced and used to determine the number of elements in such a class with special symmetries or inflation properties. The method is explained in an illustrative fashion for some widely used tiling classes with golden mean rescaling, namely for the Fibonacci chain (one-dimensional), the triangle and Penrose patterns (two-dimensional) and for Kramer's and Danzer's icosahedral tilings (three-dimensional). We obtain a rather complete picture of the orbit structure within these classes, and also discuss various general results.
- PACS
-
61.50.Ah Theory of crystal structure, crystal symmetry; calculations and modeling
- MSC
-
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
- Subjects
- Dates
-
Issue 9 (7 May 1997)
Received 9 August 1996
-
The torus parametrization of quasiperiodic LI-classes
Michael Baake et al 1997 J. Phys. A: Math. Gen. 30 3029
-
The double torus as a 2D cosmos: groups, geometry and closed geodesics
Peter Kramer and Miguel Lorente 2002 J. Phys. A: Math. Gen. 35 1961
-
Kaluza–Klein magnetic monopole in five-dimensional global monopole spacetime
A L Cavalcanti de Oliveira and E R Bezerra de Mello 2004 Class. Quantum Grav. 21 1685
-
The dielectric behaviour of single-shell spherical cells with a dielectric anisotropy in the shell
Y T C Ko et al 2004 J. Phys.: Condens. Matter 16 499
-
Localised polaronic states in mixed-valence linear chain complexes
D Baeriswyl and A R Bishop 1988 J. Phys. C: Solid State Phys. 21 339
-
Electron-impact excitation of neutral boron using the R-matrix with the pseudostates method
C P Ballance et al 2007 J. Phys. B: At. Mol. Opt. Phys. 40 1131
-
Differential equations, Frobenius theorem and local flows on supermanifolds
U Bruzzo and R Cianci 1985 J. Phys. A: Math. Gen. 18 417
-
Orbits and phase transitions in the multifractal spectrum
Thomas Nowotny et al 2001 J. Phys. A: Math. Gen. 34 1
-
Direct EIT Jacobian calculations for conductivity change and electrode movement
Camille Gómez-Laberge and Andy Adler 2008 Physiol. Meas. 29 S89
-
CPEM 2006 round table discussion 'Proposed changes to the SI'
Michael Stock and Thomas J Witt 2006 Metrologia 43 583
Related review articles
What's this?- Generalized Bernoulli-Hurwitz numbers and the universal Bernoulli numbers
- Algebraic methods for solution of polyhedra
- A property of the set of prime numbers