English

Quadrilateral reptiles

Metric Geometry 2022-05-24 v1

Abstract

A polygon PP is called a reptile, if it can be decomposed into k2k\ge 2 nonoverlapping and congruent polygons similar to PP. We prove that if a cyclic quadrilateral is a reptile, then it is a trapezoid. Comparing with results of U. Betke and I. Osburg we find that every convex reptile is a triangle or a trapezoid.

Keywords

Cite

@article{arxiv.2205.11068,
  title  = {Quadrilateral reptiles},
  author = {Miklos Laczkovich},
  journal= {arXiv preprint arXiv:2205.11068},
  year   = {2022}
}
R2 v1 2026-06-24T11:25:13.845Z