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Not only can a regular polygon have equal angles and sides, it must have them.
It is a regular polygon no doubt about it.* * * * *There is no doubt that the above answer is totally incorrect.A regular polygon must have all its sides as well as all its angles equal. The second condition is not satisfied and so a rhombus is nota regular polygon.
The interior angles of a regular polygon must be 60 degrees or greater.
A regular polygon has all its sides equal and all its angles equal. One consequence is that no angle can be reflex (between 180 and 360 degrees). A concave polygon, on the other hand, must have at least one angle that is a reflex angle. The line joining any two points inside any convex polygon (and that includes regular ones) must lie wholly within the polygon. In a concave polygon, it must be possible to find two point inside the polygon such that the line joining them crosses the boundaries of the polygon.
A 6 sided hexagon polygon can be regular or irregular.