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By definition, a regular polygon has all interior angles the same, but a concave polygon has some interior angles that are not identical. Also, it violates the axiom that all vertices lie on a circle.

While it is possible to construct a polygon with equilateral sides, to be concave would require a form that is equally convex and laterally opposite. (An example is a 'solid arrow shape.')

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Q: Why can't a concave quadrilateral be regular?
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