You could go full circle by mapping a tessellated tile-able projection like Peirce quincuncial back onto the spherical lampshade via the inverse stereographic p

You could go full circle by mapping a tessellated tile-able projection like Peirce quincuncial back onto the spherical lampshade via the inverse stereographic projection. http://www.jasondavies.com/maps/peirce/ http://www.jasondavies.com/maps/peirce/ http://math.ucr.edu/home/baez/week229.html http://math.ucr.edu/home/baez/week229.html