4 sides
No rounded areas
No gaps between lines
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what do yo mean by formulas? Are you asking for the different characteristics of quadrilaterals that make some squares and some rhombuses? There is not really a formula for a quadrilateral.
a square is a mix between a rhombus and a rectangle
Yes
Yes.
There is no special name. And some quadrilaterals with special characteristics (eg a trapezium) could still have all sides of different lengths.