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A hexagon.
Not possible. The shape will either be incomplete or have intersecting lines.
a cube * * * * * It cannot be a cube because a cube does not have 8 pairs of perpendicular faces - it has 12.
Any shape with more than 3 sides can have two pairs of equal sides and no right angles. If it only has 4 sides in total and isn't a parallelogram, then it's a trapezoid.
You can have 0, 1, 2, or 3 pairs of parallel sides in a heptagon.