Abstract
This work introduces the idea of symmetry order, which describes the rotational symmetry types of tilings in the hull of a given substitution. Definitions are given of the substitutions σ6 and σ7 which give rise to aperiodic primitive substitution tilings with dense tile orientations and which are invariant under six-and sevenfold rotations, respectively; the derivation of the symmetry orders of their hulls is also presented.
Original language | American English |
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Pages (from-to) | 388-398 |
Number of pages | 11 |
Journal | Mathematics Faculty Publications |
Volume | 74 |
Issue number | 4 |
State | Published - Jul 1 2018 |
ASJC Scopus Subject Areas
- Structural Biology
- Biochemistry
- General Materials Science
- Condensed Matter Physics
- Physical and Theoretical Chemistry
- Inorganic Chemistry
Keywords
- symmetry order
- aperiodic tilings
- substitution tilings
- rotation-invariant tilings
- dense tile orientations
Disciplines
- Geometry and Topology
- Mathematics