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Mosaics and their isometric embeddings. (English. Russian original) Zbl 1031.52007
Izv. Math. 66, No. 3, 443-462 (2002); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 66, No. 3, 3-22 (2002).
The main result of this paper is an enumeration of all mosaics \(T\) among the 165 mosaics in Chavey’s catalogue [D. Chavey, Comput. Math. Appl. 17, 147-165 (1989; Zbl 0704.05010)] such that either \(T\) or the dual mosaic \(T^*\) is embeddable in \(Z_n\) isometrically or with scale \(\lambda=2\).
Also some interesting infinite-dimensional hypermetric spaces are studied.

MSC:
52C23 Quasicrystals and aperiodic tilings in discrete geometry
05C75 Structural characterization of families of graphs
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