English

Platonic configurations of points and lines

Combinatorics 2019-07-23 v1

Abstract

We present some methods for constructing connected spatial geometric configurations (pq,nk)(p_{q}, n_{k}) of points and lines, preserved by the same rotations (and reflections) of Euclidean space E3E^{3} as the chosen Platonic solid. In this paper we are primarily interested in balanced configurations (n3),(n4)(n_{3}), (n_{4}) and (n5)(n_{5}), but also in unbalanced configurations (p3,n4),(p3,n5)(p_{3},n_{4}), (p_{3}, n_{5}) and (p4,n5)(p_{4}, n_{5}).

Keywords

Cite

@article{arxiv.1907.08751,
  title  = {Platonic configurations of points and lines},
  author = {Jurij Kovič and Aleksander Simonič},
  journal= {arXiv preprint arXiv:1907.08751},
  year   = {2019}
}