This is a "radiolaria" sculpture roughly modeled on the drawings of Ernst Haeckel. It has simple icosahedral symmetry, with thirty "spines" radiating from the edges.
The slots have been designed to accept 1/8th inch acrylic. The fit can be a little loose (not the least because acrylic sheet tends to have a little variation in thickness), so I recommend using some acrylic adhesive to hold it together when you're done.
As with all acrylic sculptures, this will be a bit brittle when assembled; try not to drop it too far. Mine is suspended from the ceiling.