You are describing a square which has all sides the same lentgh and each angle of 90 degrees.
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A square. Its opposite sides are equal and it has 4 right angles.
A shape with 4 right angles and 4 equal sides is a square. ==========================
A square has 4 equal sides, 2 pairs of parallel sides and 4 right angles.
A rectangle with 4 equal sides and angles is often called a square.
It's impossible for a quadrilateral to have no equal sides and have right angles.