STL files for printing, and a few DXF files for laser cutting. Perhaps this page is an anachronism in a post-Thingiverse world, but I started it in 2005 and it's still here.
A snap-fit puzzle of a working machine, which I designed as a commission.
A fractal-ish design which was difficult to print...or not so much to print, as to get all the holes clear afterward.
I finally got around to making a Möbius strip. It's at Shapeways.
I randomly found on YouTube a video of a dude making a guitar out of it.
A section of the gyroid surface, with a little thickness added so it's easier to visualize or build.
In this render I put a blue light on one side of the surface and a yellow one on the other. This shows how the gyroid divides space into two regions: the blue and- yellow-lit regions interlock but are separate. You should build a lamp like this.
A slightly redacted version of this, also at Shapeways. (Quite a few other people have also uploaded it there: you now behold the original.) As pictured here, this was one of the first art parts ever to be direct-metal printed.
I made this diatomaceous design using Qhull to draw a Voronoi network with the symmetry of a snub dodecahedron. A little smoothing and twisting and Bob's your uncle. This model is fanciful because of the long spines – render with confidence, print with caution.
The remaining pieces here are made to be cut and assembled from flat material. I've made this design in lasercut plywood, waterjet-cut glass, plasma-cut steel, cast silver, machined aluminum...but that was all before 3D printing.
This and the following DXF patterns are for 1/8"-thick material, but anything flat should do, provided you adjust for thickness by either scaling the whole design, or changing the width of the slots.
The assembly instructions were written for plywood kits held together with glue. If you're using a different material, they may still be useful as guides.
I had quite a few of these at one time. So many ideas that didn't make any money!