English

Cubes and adjoints of cross-polytopes

Combinatorics 2020-12-17 v1

Abstract

We describe a bijection between oriented cubes and adjoints of cross-polytopes. This correspondence is used to prove that the real affine cube is, up to reorientation in the same class, the unique oriented cube that is realizable. Moreover, its underlying matroid is, up to isomorphism, the unique combinatorial cube that is realizable over the reals.

Keywords

Cite

@article{arxiv.2012.08633,
  title  = {Cubes and adjoints of cross-polytopes},
  author = {J. Lawrence and I. P. Silva},
  journal= {arXiv preprint arXiv:2012.08633},
  year   = {2020}
}

Comments

23 pages, 4 figures

R2 v1 2026-06-23T21:00:00.990Z