A Set of Questions in Combinatorial and Metric Geometry

We briefly introduce several problems: (1) a generalization of the convex fair partition conjecture, (2) on non-trivial invariants among polyhedrons that can be formed from the same set of face polygons, (3) two questions on assembling rectangular tiles to form larger rectangles and (4) on convex regions which maximize and minimize the diameter for specified area and perimeter. For each question, we discuss partial solutions and indicate aspects that to our knowledge, await exploration.