On the separability of quadrilaterals in the plane by translations and rotations

Michael E. Houle, Godfried Toussaint

Research output: Contribution to journalArticle


A proof is given that for all positive integers n≥ 7 there exist sets of n non-overlapping quadrilaterals in the plane, such that no non-empty proper subset of these quadrilaterals can be separated from its complement, as one rigid object, by a single translation, without disturbing its complement. Furthermore, examples are given for which no single quadrilateral can be separated from the others by means of translations or rotations.

Original languageEnglish (US)
Pages (from-to)267-276
Number of pages10
JournalBeitrage zur Algebra und Geometrie
Issue number2
StatePublished - Jun 1 2017



  • Collision avoidance
  • Discrete and computational geometry
  • Interlocking polygons
  • Object mobility
  • Robotics
  • Spatial planning

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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