no
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The only shapes which will make a regular tessellation are:an equilateral trianglea squarea regular hexagon.
No, it cannot.
There are only three regular polygons which can make a regular tessellation?
There can be any number (>=3) of parallelograms in a regular hexagon. If it is not a regular hexagon you may not have any.
It is extremely difficult to explain how since it is, in fact, impossible!