truncated icosahedron frame / lampshade

Hey all,

a mathy lamp for all you geometry fans out there. it is about 30cm in diameter, though some scaling may be possible (certainly larger, to some extend smaller i would guess. for more accurate scaling use the freecad file provided and change the actual parameters)

assembly requires:

frame
50 pentagon edges
40 hexagon edges
60 connector rods

faces
12 pentagons
20 hexagons

though you may want to leave a face empty to actually put a lamp inside ;)

the bulbholder mount is meant to replace a pentagon face and works for me, you might need something else depending on the kind of socket used, hanging/standing solution etc

the faces of the lamp in the image are actually not 3d printed, but lasercut from a white 2mm acrylic sheet. I included files for printing them anyway - you may want to scale z direction to finetune translucency.

print the edges on their "roof" and support the rings from below, as shown in the screenshot. the rest should print fine without supports. tree supports on build plate only worked best for me.

Assembly: simply put two pentagon edges and one hexagon edge together and fix them in place using the connector rod. the orientation of the pentagon edge is important as it is not symmetrical --> see the images. continue working up from there, always 2x pentagon and 1x hexagon per vertex

the faces should more or less snap into place depending on your printing tolerances. in case of some loose ones hotglue is an easy solution