Problem

Source: 2007 Sharygin Geometry Olympiad Correspondence Round P6

Tags: geometry, symmetry, axes, polygon, polyhedron



a) What can be the number of symmetry axes of a checked polygon, that is, of a polygon whose sides lie on lines of a list of checked paper? (Indicate all possible values.) b) What can be the number of symmetry axes of a checked polyhedron, that is, of a polyhedron consisting of equal cubes which border one to another by plane facets?