# Reflection quasilattices and the maximal quasilattice

## Author(s): Boyle, Latham; Steinhardt, Paul J.

To refer to this page use: http://arks.princeton.edu/ark:/88435/pr10h42
DC FieldValueLanguage
dc.contributor.authorBoyle, Latham-
dc.contributor.authorSteinhardt, Paul J.-
dc.date.accessioned2019-03-27T18:28:37Z-
dc.date.available2019-03-27T18:28:37Z-
dc.identifier.citationBoyle, Latham, Steinhardt, Paul J. (2016). Reflection quasilattices and the maximal quasilattice. PHYSICAL REVIEW B, 94. doi:10.1103/PhysRevB.94.064107en_US
dc.identifier.issn2469-9950-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr10h42-
dc.description.abstractWe introduce the concept of a reflection quasilattice, the quasiperiodic generalization of a Bravais lattice with irreducible reflection symmetry. Among their applications, reflection quasilattices are the reciprocal (i.e., Bragg diffraction) lattices for quasicrystals and quasicrystal tilings, such as Penrose tilings, with irreducible reflection symmetry and discrete scale invariance. In a follow-up paper, we will show that reflection quasilattices can be used to generate tilings in real space with properties analogous to those in Penrose tilings, but with different symmetries and in various dimensions. Here we explain that reflection quasilattices only exist in dimensions two, three, and four, and we prove that there is a unique reflection quasilattice in dimension four: the “maximal reflection quasilattice” in terms of dimensionality and symmetry. Unlike crystallographic Bravais lattices, all reflection quasilattices are invariant under rescaling by certain discrete scale factors. We tabulate the complete set of scale factors for all reflection quasilattices in dimension d > 2, and for all those with quadratic irrational scale factors in d = 2.en_US
dc.language.isoen_USen_US
dc.relation.ispartofPHYSICAL REVIEW Ben_US
dc.rightsFinal published version. Article is made available in OAR by the publisher's permission or policy.en_US
dc.titleReflection quasilattices and the maximal quasilatticeen_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1103/PhysRevB.94.064107-
dc.date.eissued2016-08-25en_US
dc.identifier.eissn2469-9969-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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