An infinite number, as those four sides can be shrunk, grown, twisted, and changed an infinite number of times.
The number of types of four-sided shapes are finite, however:
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No, there are many four sided shapes. The Square is one of them. Others include rectangle,trapezoid, parellelogram, and rhombus
Quadrilaterals.
There are many such shapes and there is no specific name.
Impossible shapes. They are four sided shapes with three sides!
Quadrilaterals