Deza, M.; Shtogrin, M. I. 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. Reviewer: M.Stojanovic (Beograd) Cited in 4 Documents MSC: 52C23 Quasicrystals and aperiodic tilings in discrete geometry 05C75 Structural characterization of families of graphs Keywords:isometric embeddings; mosaics; infinite-dimensional hypermetric spaces PDF BibTeX XML Cite \textit{M. Deza} and \textit{M. I. Shtogrin}, Izv. Math. 66, No. 3, 443--462 (2002; Zbl 1031.52007); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 66, No. 3, 3--22 (2002) Full Text: DOI