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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No.
No. There can be no regular concave polygon.
concave
A chevron or arrowhead.
A concave quadrilateral. An arrowhead or a delta, for example.