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Gummelt versus Lück decagon covering and beyond. Implications for decagonal quasicrystals
Author(s) -
Steurer Walter
Publication year - 2021
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.742
H-Index - 83
ISSN - 2053-2733
DOI - 10.1107/s2053273320015181
Subject(s) - quasicrystal , unit (ring theory) , combinatorics , mathematics , crystallography , geometry , chemistry , mathematics education
Specific structural repeat units can be used as quasi‐unit cells of decagonal quasicrystals. So far, the most famous and almost exclusively employed one has been the Gummelt decagon. However, in an increasing number of cases Lück decagons have been found to be more appropriate without going into depth. The diversities and commonalities of these two basic decagonal clusters and of some more general ones are discussed. The importance of the type of underlying tiling for the correct classification of a quasi‐unit cell is demonstrated.