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You don't. If you fold it in half you can fit it into a C5 envelope.

Within this entire system, its all about succesive halvings. So folding into thirds (which is horribly difficult to do) is never needed.

That's not true, the most common envelope at least in Germany is DL for DIN Long [1], which requires folding A4 in thirds and there is a corresponding DIN norm on how to print fold marks to aid the folding in thirds [2]

[1] https://de.m.wikipedia.org/wiki/DIN_lang

[2] https://de.m.wikipedia.org/wiki/Falzmarke

Not only difficult, but prone to being sliced when using a paper opener. Paper folded in four should be placed in the envelope with the fold at the bottom so that it doesn't get cut when slicing the paper at the top of the envelope.

Unfolded