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Convex bodies which tile space by translation: Acknowledgement of priority

Published online by Cambridge University Press:  26 February 2010

P. McMullen
P. McMullen
Affiliation:
University College London, Gower Street, London WC1E 6BT.
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Extract

Since my article McMullen [1980] has appeared, Professors S. S. Ryškov and B. B. Venkov have drawn my attention to two previously published papers. B. A. Venkov [1954] proves my main Theorem 1 (and its corollary Theorem 2) by methods apparently very similar to mine (1 have not checked all the details), while A. D. Aleksandrov [1954] generalizes Venkov's result to tilings of spaces of constant curvature by polytopes (not necessarily convex) congruent to ones in some finite collection. I am happy to acknowledge their priority.

Type
Research Article
Information
Mathematika , Volume 28 , Issue 2 , December 1981 , pp. 191
Copyright
Copyright © University College London 1981

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References

Aleksandrov, A. D.. “On filling of space by polytopes”, Vestnik Leningrad. Univ. (Ser. Mat. Fiz. Him.) 9 (1954), 33–43 (Russian). MR 20 #1301.Google Scholar
Aleksandrov, A. D.. Konvexe Polyeder (Akademie Verlag, Berlin, 1958) (translated from Russian edition, 1950).Google Scholar
McMullen, P.. “Convex bodies which tile space by translation”, Mathematika, 27 (1980), 113–121.CrossRefGoogle Scholar
Venkov, B. A.. “On a class of euclidean polytopes”, Vestnik Leningrad. Univ. (Ser. Mat. Fiz. Him.) 9 (1954), 11–31 (Russian). MR 20 #1302; Zbl. 56, 141 (see Uspehi Mat. Nauk 9 (1954), no. 4 (62), 250-251, which also refers to Aleksandrov [1954]).Google Scholar