Mathematika

Research Article

Convex bodies which tile space by translation: Acknowledgement of priority

P. McMullena1

a1 University College London, Gower Street, London WC1E 6BT.

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.

(Received April 01 1981)

Key Words:

  • 52A45: CONVEX SETS AND GEOMETRIC INEQUALITIES; Packings, covering, tiling