The almost unpronounceable Peirce Quincuncial projection (kwin-kun-shal) is undoubtedly a thing of beauty. Created in 1879 by American Charles Sanderson Pierce (the 'Father of Pragmatism', according to Wikipedia), it places the North Pole at its centre, and the South Pole precisely nowhere, though very almost in all four of the corners. This means that, for the fans of tessellating amongst you, you can tile this projection ad infinitum.
The 'quincuncial' refers to the fact that each hemisphere has been divided into four quadrants. In this case, the Northern hemisphere's four quadrants have been collected together, whilst the southern four are scattered. That's either classic Global North bias for you, or a sensible portrayal of a world where far 68% of the land is found in the northern hemisphere. Up to you.
The Peirce Quincuncial does not maintain true directions or distances (so not one for orienteering), and area distortion grows from the centre of the square outwards. As you can probably see, what we call 'conformality' vanishes in the middle of the four edges, where all the angles - which are otherwise true - finally go to pot. Helpfully, this graticular chaos is limited to the middle of oceans, but not before doing its best to pull West Africa down with it.
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• Paper thickness: 10.3 mil
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• Hanging hardware included