Yes a square will tessellate on its own
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Tessellation is defined as the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellations can be generalized to higher dimensions. A periodic tiling has a repeat pattern. A regular quadrilateral can be used by itself to make a tessellation.
Because it has 4 equal sides. * * * * * No. That is not enough to make it a regular quadrilateral. A regular polygon must also have equal angles and a rhombus, in general, does not.
No, it is not possible.
A quadrilateral is a polygon with 4 sides... so if it has 4 sides it is a quadrilateral. your question doesnt make sense because a 4 sided quadrilateral could be any quadrilateral at all.
Any polygon with 4 sides is a quadrilateral