How to Make Your Own Tessellation: Flipping

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Sometimes a tessellation artist flips lines, or shapes, horizontally or vertically - why?

It gives us a different symmetrical pattern. (See more about symmetry here.) For example, in DIY line example 1,pictured below, instead of just rotating the second line, let's flip it horizontally too. Note the markers a & b. It looks nearly the same in this case as the line, by chance, is almost symmetrical but now...