### Abstract

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 language | English (US) |
---|---|

Pages (from-to) | 267-276 |

Number of pages | 10 |

Journal | Beitrage zur Algebra und Geometrie |

Volume | 58 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1 2017 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory
- Geometry and Topology