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They are simply four pairs of perpendicular lines. There is nothing in the question to suggest there is anything more than that to them.
Draw three lines separating the four columns and then draw three more lines separating the rows
A regular hexagon has more than 4 lines of symmetry. Even number sided polygons that are regular and have more than 4 sides have more than 4 lines of symmetry. Circles have more than four lines of symmetry. Squares also have 4 lines of symmetry.
A square has four lines of mirror symmetry: the lines connecting the centers of opposite sides and the lines connecting opposite vertexes. A regular hexagon has six, with the same definitions.
Yes, a square has four vertices. A vertex is a point in which two or more lines intersect.