Geodesic
Symmetry of Three-dimensional Quasicrystals
The relation between the three-dimensional quasicrystal models, the one by Penrose transformation method which was found by the author in 1985 and the other by the so-called projection method, is clarified. Primitive projection model is formulated as a mapping from a region in the pseudospace to the physical space by introducing the concept of the gazing crystal. It makes it possible to study the structure of the so­called projection method in detail. In conclusion, the primitive projection model, being deterministic, is included in the Penrose transformation model in the widest sense, which, having some freedom, is more flexible to realize some hierarchical local symmetries.
Classification : 52C23 
@article{VM_1999_1_4_a4,
     author = {Tohru Ogawa},
     title = {Symmetry of {Three-dimensional} {Quasicrystals}},
     journal = {Visual Mathematics},
     publisher = {mathdoc},
     volume = {1},
     number = {4},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VM_1999_1_4_a4/}
}
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%A Tohru Ogawa
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Tohru Ogawa. Symmetry of Three-dimensional Quasicrystals. Visual Mathematics, Tome 1 (1999) no. 4. http://geodesic.mathdoc.fr/item/VM_1999_1_4_a4/