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PreprintarXiv licencearXiv

Reconstruction of slices of cubes

  • Marie-Charlotte Brandenburg
  • Juliana Curtis
  • Chiara Giardino
  • Chiara Meroni
  • Arnau Padrol
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Abstract

We prove that the combinatorial type of a slice of the cube by a hyperplane is completely determined by its graph, within the class of cube slices. We also show that such a result cannot extend to slices of arbitrary simple polytopes by constructing a simple polytope that has two combinatorially distinct slices with isomorphic graphs.

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Cite

BibTeXRIS
BibTeX
@misc{brandenburg2026reconstruction,
  title = {{Reconstruction of slices of cubes}},
  author = {Marie-Charlotte Brandenburg and Juliana Curtis and Chiara Giardino and Chiara Meroni and Arnau Padrol},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.09939},
  eprint = {2610.09939},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.09939},
}
RIS
TY  - UNPB
TI  - Reconstruction of slices of cubes
AU  - Marie-Charlotte Brandenburg
AU  - Juliana Curtis
AU  - Chiara Giardino
AU  - Chiara Meroni
AU  - Arnau Padrol
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.09939
UR  - https://arxiv.org/abs/2610.09939
AB  - We prove that the combinatorial type of a slice of the cube by a hyperplane is completely determined by its graph, within the class of cube slices. We also show that such a result cannot extend to slices of arbitrary simple polytopes by constructing a simple polytope that has two combinatorially distinct slices with isomorphic graphs.
ER  -