Quasicrystal Tilings in Three Dimensions and Their Empires
AbstractThe projection method for constructing quasiperiodic tilings from a higher dimensional lattice provides a useful context for computing a quasicrystal’s vertex configurations, frequencies, and empires (forced tiles). We review the projection method within the framework of the dual relationship between the Delaunay and Voronoi cell complexes of the lattice being projected. We describe a new method for calculating empires (forced tiles) which also borrows from the dualisation formalism and which generalizes to tilings generated projections of non-cubic lattices. These techniques were used to compute the vertex configurations, frequencies and empires of icosahedral quasicrystals obtained as a projections of the
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Hammock, D.; Fang, F.; Irwin, K. Quasicrystal Tilings in Three Dimensions and Their Empires. Crystals 2018, 8, 370.
Hammock D, Fang F, Irwin K. Quasicrystal Tilings in Three Dimensions and Their Empires. Crystals. 2018; 8(10):370.Chicago/Turabian Style
Hammock, Dugan; Fang, Fang; Irwin, Klee. 2018. "Quasicrystal Tilings in Three Dimensions and Their Empires." Crystals 8, no. 10: 370.
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