Convex Bodies which Tile Space

  • P. McMullen
Conference paper

Abstract

We say that the convex body (compact convex set with nonempty interior) K tiles d-dimensional Euclidean space E d (by translation) if there is some family T of translation vectors, such that (i) K covers E d , and (ii) if t i T (i = 1,2) with t 1t 2, then K + t 1 and K + t 2 have disjoint interiors; that is, K is simultaneously a covering and packing of E d . We call K a tiling of E d (by translation), and call K and its translates in K tiles. A particularly important case is when T is a lattice (discrete additive subgroup of E d ), when we call K a lattice tiling.

Keywords

Hull Stein Delone 

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Copyright information

© Springer-Verlag New York Inc. 1981

Authors and Affiliations

  • P. McMullen
    • 1
  1. 1.University CollegeLondonEngland

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