Finiteness conjecture for resistance-positive simple 3-polytopes
Finiteness conjecture for resistance-positive simple 3-polytopes
Let a polytope be resistance-positive when its resistance curvature is positive at every vertex. Finiteness conjecture for resistance-positive simple 3-polytopes. There are finitely many simple -dimensional polytopes that are resistance-positive and are not isomorphic to a prism over a polygon.
The conjecture is motivated by degree-based criteria forcing nonpositive resistance curvature and would establish scarcity of resistance-positive simple -polytopes beyond prisms over polygons. The source gives no resolution of this question.
Sources & referencesView supporting material
Primary source
Jesús A. De Loera, Jillian Eddy, Sawyer Jack Robertson and José Alejandro Samper, “Discrete Curvatures and Convex Polytopes”, arXiv:2510.11894 (2025).
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