A 'grasshopper' script with three formulas created this purely mathematically formed surface. Out of a multitude of variations I chose this one - SP-14 - and developed a 3D printable lampshade out of it.
The diameter measures 20 and the height 25 cm. This is big enough for a standard LED bulb with 10.5 Watt.
The handling is very easy, you first push the shade over the socket with the bulb far up and then put the clip over the socket. Now you lower the lamp shade again and your new lamp is ready!
You can print both parts with a large nozzle (0.8-1.2 mm) in vase mode without support structure. You should anchor the shade with a wide edge (brim) on the printing plate, otherwise it will eventually come loose.
Have fun with 3D printing!
Antonin T. Clark