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I'm looking for the ESPG code of this projection.

enter image description here

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It looks like a Peirce Quincuncial:

https://en.wikipedia.org/wiki/Peirce_quincuncial_projection

I don't see it in the EPSG registry, but you could make up a PROJ string or WKT for it from the examples here:

https://proj.org/en/9.2/operations/projections/peirce_q.html

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