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Is it possible to visualize EPSG:102020 and EPSG:3857 at same time in QGIS? If is possible, how?

Why some EPSG permit on the fly transformation and visualization and other don`t?

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There are two issues with what you are trying to do here, first EPSG:102020 is not really an EPSG code it is an ESRI code so there is always a risk that non ESRI software will be unable to handle it.

The second and more fundamental one is that ESRI:102020 is a (south) polar projection while EPSG:3857 is a Transverse Mercator projection which goes to infinity at the poles so it is not able to show the polar regions which is what is being shown in your other data set.

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