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arXiv · 2609.25181

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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Juliana Curtis, Tuong Le, Chayim Lowen. 2026-09-21. On Smooth Combinatorial Products of Simplices. https://arxiv.org/abs/2609.25181

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