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I am writing documents that are going to be printed. Therefore I like using the twoside option of the geometry package in order to get the alternating page margins which allow me to easily bind them.

My problem is that I am not using a book cover. Therefore the first page in the document is going to be the cover page.

The geometry package assumes that the first page is going to be at the back of the cover page which is why the first page (and all following, odd pages) have the bigger margin to the left of the side.

How can I swap this behavior so that odd pages have the larger margin to the left and the even ones to the right but still keep the page numbering intact (I know that I can simply start the page numbering at 2 in order to achieve this but that doesn't make much sense for anyone looking at the printed document)?

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    Set the bindingoffset, see the docu of geometry. – Ulrike Fischer Apr 28 '18 at 12:55
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My question has been answered in the comments by Ulrike Fischer, but for the sake of completeness I will post it as an "official" answer to my question.

It turned out that what I actually wanted was to set a bindingoffset which is another option in the geometry package. In combination with the asymmetric (instead of twoside) option this did exactly what I needed.

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