Yes.
it seems to me that the only polygon of your description is a square
They are regular polygons such as a square and an equilateral triangle
A square is a regular polygon because all sides are equal and all angles are equal.
It is then classed as a regular polygon such as a square or an equilateral triangle.
No but a square is because it has equal side lengths and equal interior angles
A square is a regular quadrilateral polygon because it has 4 equal sides and 4 equal right angles
Square or rectangle
Only when the polygon is a regular convex polygon. Such as an equilateral triangle, or a square, or a regular pentagon.
A regular polygon is a polygon in which all sides and angles are congruent, so a rectangle is a regular polygon when it is a square: when all sides are equal.
A regular polygon (a closed plane figure of straight lines) has all equal angles and all equal side lengths. For example, a square is a regular quadrilateral, because it's four edges are all the same length, and it's angles are all equal (90 degrees). A regular triangle is an equilateral triangle.An irregular polygon does not have equal sides and angles. N.B to be regular, a polygon must have both equal sides and equal angles. If a polygon has equal sides but unequal angles it is not a regular polygon.
A regular polygon has equal angles AND sides.
4 such as a square