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A square, by definition, must have four right angles. A plane shape with 4 right angles which is not a square is a rectangle.
It is impossible to have a six sided shape with right angles since the lines would never meet, therefore it would not create a shape. The most right angles you can have in a shape is four. A six sided shape is called a hexagon. There are Regular Hexagons, meaning all the sides and all the angles are equal. Any other Hexagon with unequal sides and angles and called Irregular Hexagons. Each side must be straight, and the sum of the angles equaling 720°.
A rhombus has 4 equal sides. Its angles can be right angles, but don't have to be. A square is a type of rhombus.
An irregular hexagon.
Well, honey, that would be rectangles. Those four-sided figures have diagonals that are equal in length and intersect at right angles outside the shape. So, if you're looking for a shape with some perpendicular diagonal action, rectangles are where it's at.