A sphere.
shape no pairs of perpendicular sides
A shape with three and only three sides is a triangle, but it is not possible for a triangle to have three perpendicular sides.
It is not possible to have five perpendicular sides; four or eight, but not five. A shape with five equal sides is a pentagon.
No sides perpendicular means no right angles. A rhombus is a quadrilateral with no right angles so no sides perpendicular.
A right angled triangle is an example of a shape with exactly 2 perpendicular sides.
square
a Kite
A shape with a pair of perpendicular sides is a rectangle. In a rectangle, opposite sides are equal in length, and adjacent sides meet at right angles, forming perpendicular intersections. Other shapes that also feature perpendicular sides include squares and right triangles.
The first geometric shape that comes to mind with no perpendicular sides is a triangle.
No anwser impossible
A hexagon.
parallelogram