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No it is not. On a number of counts.

A polygon is an enclosed plane area whose boundaries comprise straight lines. It is, therefore, a 2-dimensional object and so does not have faces. If you meant sides instead, the answer is still NO. If all the sides and and angles are congruent then the polygon MUST be convex.

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Q: Is a polygon that has all congruent faces and angles a concave polygon?
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