There are infinitely many possible answers. For example, any regular polygon with an even number of sides.
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shape no pairs of perpendicular sides
I suppose. All of a square's sides are perpendicular.
Diamonds come in all shapes and sizes, which determine the number of perpendicular lines (assuming you are referring to the edges as the lines) so there is no one number of lines or perpendicular lines on a diamond.
A polygon with only 1 pair of perpendicular sides is called a trapezoid. In a trapezoid, one pair of opposite sides are parallel, while the other pair are not parallel and intersect at a right angle. The sum of the interior angles of a trapezoid is always 360 degrees. Examples of trapezoids include isosceles trapezoids, right trapezoids, and scalene trapezoids.
A triangle has no parallel sides but a right angle triangle has perpendicular sides that meet at 90 degrees.