Two finiteness theorems for periodic tilings of d-dimensional euclidean space

Dolbilin NP, Dress A, Huson DH (1998)
Discrete & Computational Geometry 20(2): 143-153.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Dolbilin, Nikolai Petrovich; Dress, AndreasUniBi; Huson, Daniel H.
Abstract / Bemerkung
Consider the d-dimensional euclidean space E-d. Two main results are pre sented: First, for any N is an element of N, the number of types of periodic equivariant tilings (T, Gamma) that have precisely N orbits of (2, 4, 6,...)-flags with respect to the symmetry group Gamma, is finite. Second, for any N is an element of N, the number of types of convex, periodic equivariant tilings (T, Gamma) that have precisely N orbits of tiles with respect to the symmetry group Gamma, is finite. The former result (and some generalizations) is proved combinatorially, using Delaney symbols, whereas the proof of the latter result is based on both geometric arguments and Delaney symbols.
Erscheinungsjahr
1998
Zeitschriftentitel
Discrete & Computational Geometry
Band
20
Ausgabe
2
Seite(n)
143-153
ISSN
0179-5376
Page URI
https://pub.uni-bielefeld.de/record/1625193

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Dolbilin NP, Dress A, Huson DH. Two finiteness theorems for periodic tilings of d-dimensional euclidean space. Discrete & Computational Geometry. 1998;20(2):143-153.
Dolbilin, N. P., Dress, A., & Huson, D. H. (1998). Two finiteness theorems for periodic tilings of d-dimensional euclidean space. Discrete & Computational Geometry, 20(2), 143-153. doi:10.1007/PL00009380
Dolbilin, N. P., Dress, A., and Huson, D. H. (1998). Two finiteness theorems for periodic tilings of d-dimensional euclidean space. Discrete & Computational Geometry 20, 143-153.
Dolbilin, N.P., Dress, A., & Huson, D.H., 1998. Two finiteness theorems for periodic tilings of d-dimensional euclidean space. Discrete & Computational Geometry, 20(2), p 143-153.
N.P. Dolbilin, A. Dress, and D.H. Huson, “Two finiteness theorems for periodic tilings of d-dimensional euclidean space”, Discrete & Computational Geometry, vol. 20, 1998, pp. 143-153.
Dolbilin, N.P., Dress, A., Huson, D.H.: Two finiteness theorems for periodic tilings of d-dimensional euclidean space. Discrete & Computational Geometry. 20, 143-153 (1998).
Dolbilin, Nikolai Petrovich, Dress, Andreas, and Huson, Daniel H. “Two finiteness theorems for periodic tilings of d-dimensional euclidean space”. Discrete & Computational Geometry 20.2 (1998): 143-153.

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