Hexagon
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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.
Any polygon with more than 5 sides can do that.
Most shapes will have more than two sides. If the sides are straight lines, the shapes MUST have more than two sides.
A shape with four sides has more vertices because there are more points where edges (straight lines) meet than a 3-sided shape.
hexagon, heptagon