No, a square is a quadrilateral, and a hexagon has six sides, hense, hex meaning six, and a square is a quadrilateral, quad meaning four.
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Neither a square nor a hexagon are rigid so the question is misguided. Any square can be "squashed" into a rhombus and a hexagon into an irregular hexagon. The only rigid polygon is a triangle.
A square has 4 sides, and a hexagon has 6 sides. Therefore, a square and a hexagon together have a total of 10 sides.
A hexagon has more vertices.
six
Why