A regular polygon is one in which:

A regular polygon is one in which:
  1. All sides are equal but angles may differ
  2. All angles are equal but sides may differ
  3. All sides and all angles are equal
  4. It has at least one pair of parallel sides

Solution

A polygon is regular only if it is both equilateral (all sides equal) and equiangular (all angles equal).

Asked in: IMO

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