Geometric models for continuous transitions from quasicrystals to crystals
- 1 April 1989
- journal article
- research article
- Published by Taylor & Francis in Philosophical Magazine Letters
- Vol. 59 (4) , 181-188
- https://doi.org/10.1080/09500838908206341
Abstract
Starting from variable p-vectors half-stars which verify Hadwiger's theorem, the cut-projection method is used here. The strip of projection is projected on a rotatory subspace and a variable tiling is obtained. Two outstanding examples are developed. The first, a continuous evolution from a two-dimensional octagonal quasilattice to two square lattices 45° rotated in between. The second is a continuous evolution from a three-dimensional Penrose tiling to an f.c.c. vertex lattice. Physical applications to quasicrystal-crystal transitions are pointed out.Keywords
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