Physics – Mathematical Physics
Scientific paper
2006-06-09
Nankai Tracts in Mathematics, Vol. 10, (World Scientific, Singapore, 2006), pp. 123-132
Physics
Mathematical Physics
LaTeX2e, 11 pages, 6 eps figures, 23rd International Conference of Differential Geometric Methods in Theoretical Physics, Nank
Scientific paper
We show that generalized Penrose tilings can be obtained by the projection of a cut plane of a 5-dimensional lattice into two dimensions, while 3-d quasiperiodic lattices with overlapping unit cells are its projections into 3d. The frequencies of all possible vertex types in the generalized Penrose tilings, and the frequencies of all possible types of overlapping 3-d unit cells are also given here. The generalized Penrose tilings are found to be nonconvertable to kite and dart patterns, nor can they be described by the overlapping decagons of Gummelt.
Au-Yang Helen
Perk Jacques H. H.
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