Corpus ID: 15659488

Extremal antipodal polygons and polytopes

@article{Aichholzer2013ExtremalAP,
  title={Extremal antipodal polygons and polytopes},
  author={Oswin Aichholzer and Luis Evaristo Caraballo and Jos{\'e} Miguel D{\'i}az-B{\'a}{\~n}ez and Ruy Fabila Monroy and Carlos Ochoa and P. Nigsch},
  journal={ArXiv},
  year={2013},
  volume={abs/1301.6667}
}
  • Oswin Aichholzer, Luis Evaristo Caraballo, +3 authors P. Nigsch
  • Published 2013
  • Computer Science, Mathematics
  • ArXiv
  • Let S be a set of 2n points on a circle such that for each point p 2 S also its antipodal (mirrored with respect to the circle center) point p 0 belongs to S. A polygon P of size n is called antipodal if it consists of precisely one point of each antipodal pair (p;p 0 ) of S. We provide a complete characterization of antipodal polygons which maximize (minimize, respectively) the area among all antipodal polygons ofS. Based on this characterization, a simple linear time algorithm is presented… CONTINUE READING

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