No. A polygon can be symmetric but need not be. In fact, the majority of polygons are not symmetrical.
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No but an isosceles trapezoid is symmetrical.
32. 16 through opposite vertices and 16 through the centres of opposite sides.
example of symmetrical distribution
it seems to me that the only polygon of your description is a square
A type of polygon is a rhombusial polygon, trysectalnict polygon, and a equilateral polygon.