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Depending on how far you fold the corners, you may end up with a smaller square/diamond, or an irregular octagon.
If a diamond does not necessarily have to have right angles in it, but if it does then all four corners have to be right angles. Think of a diamond as a turned square or rhombus.
how much some thing is
A quadrilateral. There are numerous quadrelaterals including a square, a rectangle, a diamond etc
There is no set rule establishing the angles on a diamond; even a square (all four corners 90•) turned on edge is a diamond. Generally, a diamond is considered to have two angles less than 90• and two angles greater than 90•, that's it.