A very nice alternative world projection, the butterfly projection.
You have probably guessed, my favourite map projection is the Butterfly. Its core idea is to divide the Earth into eight octants. An octant is an eights of a solid in this case a sphere. Each octant can then be “flattened” and arranged into a unified area.
Links:
Explaining how https://medium.com/@borism/how-to-make-a-beautiful-map-6d6776a20a48
Explanation of how they created it https://interface.fh-potsdam.de/butterfly/