  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.
