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PreprintarXiv licencearXiv

On Smooth Combinatorial Products of Simplices

  • Juliana Curtis
  • Tuong Le
  • Chayim Lowen
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Abstract

We show that every lattice weak Minkowski summand of a smooth polytope combinatorially isomorphic to a product of simplices has a quadratic triangulation. This is achieved by identifying this class of polytopes with the class of Nakajima polytopes. We combine these results to give a new proof that two lattice weak Minkowski summands of the same such smooth polytope are relatively IDP. Along the way, we prove a structure theorem for simple polytopes whose 2-faces are triangles and trapezoids.

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Cite

BibTeXRIS
BibTeX
@misc{curtis2026smooth,
  title = {{On Smooth Combinatorial Products of Simplices}},
  author = {Juliana Curtis and Tuong Le and Chayim Lowen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25181},
  eprint = {2609.25181},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25181},
}
RIS
TY  - UNPB
TI  - On Smooth Combinatorial Products of Simplices
AU  - Juliana Curtis
AU  - Tuong Le
AU  - Chayim Lowen
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.25181
UR  - https://arxiv.org/abs/2609.25181
AB  - We show that every lattice weak Minkowski summand of a smooth polytope combinatorially isomorphic to a product of simplices has a quadratic triangulation. This is achieved by identifying this class of polytopes with the class of Nakajima polytopes. We combine these results to give a new proof that two lattice weak Minkowski summands of the same such smooth polytope are relatively IDP. Along the way, we prove a structure theorem for simple polytopes whose 2-faces are triangles and trapezoids.
ER  -