6 problems

Continuous blooming conjecture. Every convex polyhedral boundary has a continuous blooming.

Equivistal subdivision conjecture. The equivalence relation induced by equivistality constitutes a convex polyhedral subdivision of $S$. Moreover, the number of open regions in thi…

Polynomial combinatorial-type conjecture. The cardinality of the set of combinatorial types of shortest paths in $S$ is polynomial in the number of facets of $S$ when the dimension…

Higher-dimensional parallelogram decomposition conjecture. Every surface in

Let the geodesic complexity of a convex polyhedron mean the minimum number of sets needed to cover its geodesic motion-planning problem, so that a complexity of at most four means…

Let the geodesic complexity of a convex polyhedron mean the minimum number of sets needed to cover its geodesic motion-planning problem, so that a complexity of at least four means…