The load path that keeps the upper part floating took me a while to figure out. 

The first time I saw this concept was on Dave Garaway’s channel 4 “Today” show, c 1950.  It may have been made from ceramic and string.

Three pieces press-fit together to form each triangle.  They have a nice press fit, with a clearance of 0.2 mm between surfaces.

I tried a variety of materials for the strings.  PLA pulled from a hot nozzle was surprisingly strong. Ended up using strands of copper wire from a flexible extension chord.  Each wire end was wrapped around a small scrap of PLA to prevent pull-out from the triangle.