Welcome onto the Peanut planet. A planet with an angle of view of 720°, where each people appear twice (at least), and where one circular plate became square. Compare to the straight stereographic projection.The original equirectangular panorama is here.
This projection is built in the same way as Seb built his 720° panoramas, but using an oblique mercator projection instead of the straight one as the intermediate step. (Also I didn't have two different 360° panoramas of the same place, so I repeated the same.)
Part of my Wee planets set.