This is a truncated Icosahedron created by friction welding 20 hexagons together.
The individual hexagons are printed separately. After printing the hexagons they are welded together using a Dremel rotary tool and a small section of printer filament. The friction welding process works for PLA, ABS, 1.75mm and 3mm filament.
More information on the process used for friction welding this thing is available here: http://www.scorchworks.com/Blog/friction-welding-with-a-dremel-rotary-tool/
EDIT: I updated the SCAD file to make it more easily adjustable from a hexagon to other shapes and added comments.