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.
References
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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