Geodesic
$4$-crystals and quasicrystals
Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 1, pp. 28-35.

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$4$-crystals are periodic material structures in the $4$-dimensional space-time. The classical crystallographic relations are generalized to this case. The quasicrystals are solids whose X-ray photograph and electronogram contain regular pentagons. It is shown that the quasicrystals obtained experimentally by Shechtman et al. are $4$-crystals.
Keywords: crystal, polarizability, symmetry. 
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R. M. Garipov; M. S. Kotel'nikova. $4$-crystals and quasicrystals. Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 1, pp. 28-35. http://geodesic.mathdoc.fr/item/SJIM_2014_17_1_a3/

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