Conjecture on local Rupertness of trapezohedra and reverse Rupertness of antiprisms

A polyhedron is locally Rupert if it admits a Rupert passage after an arbitrarily small alteration of a suitable orientation, and locally reverse Rupert is the analogous reverse-passage property. A trapezoidal polygonal section is a section of a polyhedron that is a trapezohedron's defining polygonal section, while an antiprism section is a section with antiprism structure. Local trapezohedron–antiprism conjecture. Trapezohedra are locally Rupert and antiprisms are locally reverse Rupert. Furthermore, there are bootstrap lemmas for these infinite classes showing that every polyhedron $Q$ with a trapezoidal polygonal section is locally Rupert and every polyhedron $Q$ with an antiprism section is locally reverse Rupert. The conjecture is presented as further work: the required local results and bootstrap lemmas are not established in the paper, although the Cube and Octahedron provide motivating examples.