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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

Convex Body Translation Vector Finite Union Star Body Dimensional Face 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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