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It works out that a polygon with 1175 diagonals has 50 sides
no
square and rectangle
Regular polygons with even sides if there are 6 or more of them; selected irregular polygons with seven or more odd numbers of sides.
Any regular polygon. Lots of irregular polygons can also have congruent diagonals, for example a kite. The answer should not be "a square" because it is a rectangle - a special case but a rectangle nevertheless.