These are simple regular solids that are, well, solid. They may actually use less material than the hollow dodecahedron at thingiverse.com/thing:198 if you let skeinforge do its thing. (I didn't actually check.)

These are two of the basic shapes in pyTopMod, except that it builds them edge down. If there's a way to align faces in TopMod, I didn't find it. I used blender to rotate them to be face down.

I also tried TopMod's soccer ball, but it has too much overhang and failed to build.

The whistle is in the picture because I built the plain whistle thingiverse.com/thing:1222 and built a 1cm icosahedron first and dropped it in during build.

A decorative thimble designed in TopMod, using the method described in the shotglass tutorial which is linked from the shotglass object:
thingiverse.com/thing:434
After TopMod (the .obj file), this was resized and converted to .dae using Meshlab so that it could be printed by Shapeways. Here is the object at Shapeways:
shapeways.com/model/27961/collector_s_thimble.html
This was basically my first attempt at 3D design; the tutorial was extremely helpful.
I'd be curious if anyone tries to print this with Makerbot or RepRap. One note is that it lacks the support between the inner and outer layers that is described in the shotglass tutorial, so I imagine that would need to be added. I think the thinnest surfaces and smallest gaps are a bit under 2mm. The outer dimensions are a bit large for a thimble; that was so that Shapeways could print it (my first attempt had been too thin).

TMR posited it might take half an hour to make a d20 in Sketchup... it took 35-40 minutes, including figuring out a good process.

For the record, I used TopMod to generate the original twenty-face regular solid (it's an icosahedron, I believe, but my memory may be faulty), and I also cleaned up in Meshlab (couple clicks just to make sure the mesh was ok).

It Skeined great, at least for the jumbo size dice.

Over the top tea pot showing some easy flourishes from TopMod, based on the basic tea pot I uploaded earlier:

thingiverse.com/thing:451

An exercise in some new techniques and just plain campy fun.

Felt like doing something a bit more complicated than a cup, so I went for a teapot.

All shaped in TopMod, subdivided/smoothed in Blender.

I'll be working on variants of this for a while... improving the spout, adding a mesh to hold the tea leaves back, and internal supports so it can be printed as is.

Took some finicky fiddling but finally got a hand-drawn Klein bottle with all the normals going the right way, and was able to import it into TopMod and play with it.

The 'simplest' variant has not been subdivided in any way... it's a good starting point if you want to adjust the overall shape.

The 'skin' variant has been subdivided using the Doo Sabin remeshing option in TopMod, giving it a rounded, smooth look. It might make a very infuriating teapot, I suppose.

The 'bone' variant is the same as the 'skin', but with more visibility inside.

To get a good idea of what is going on inside, some of the pictures of the wireframe views of these Things are your best bet.

So this answers the question: Yes, we can make a Klein bottle.

EDIT: Added an anaglyph image, since this is a confusing shape. Getcher red'n'blue glasses, step right up!

A deceptively complex little holder for your next soft-boiled egg, or that collectible autographed baseball. It looks like a simple plastic utensil until you examine it more closely, and look inside.

The outer shell is smooth, with a few softly rounded holes in it, but it's held up by columns half-hidden inside, as is the floor of the well in the center.

Something a bit more practical made with TopMod, and with a direct reference to RepRap myth and lore: an organic, topologically generated shotglass which should print just fine in a RepRap or MakerBot but be a bit more interesting than the usual spent-ammo-casing tubes...

Afterall, who wants to toast a new 3D printer with something you could make in a lathe or in a mold?

EDIT: Added a variant with a twist. Same licence, download, modify, print... or do what TMR did and make your own from scratch after you see the tutorial video!

EDIT: Added a variant with a flat base and a diamond pattern in the filigree, as per Zach's suggestions. It should print more cleanly.

EDIT: It slices in Skeinforge, and it prints on a MakerBot. Screenshot added.

Still on a TopMod bender, sorry. Hopefully will work it out of my system soon enough.

This one is the top half of an octahedron, or a square-base pyramid, given an organic skeleton look. I was going for something simpler and beefier in an effort to come closer to something reasonable for a MakerBot. Doesn't really respect the 45 degree rule 100%, tho.

Another, more solid TopMod experiment which may be printable without supports.

This one starts with a dodecahedron, turns it into a first order menger sponge ( en.wikipedia.org/wiki/Menger_sponge Yes, they don't HAVE to be based on cubes... ) and then plays some additional games with it.

Yet another experiment in TopMod.

This time I really went overboard and I don't think there is a way to print this without adding supports. In fact, you probably need one of those machines that sinters a powder layer by layer... like the CandyFab.

Still, I liked how it looked so I thought I'd share. If this doesn't meet rule number one (a real, physical object that can be made), I'll take it down.

Another TopMod experiment, just working out the workflow between TopMod and Blender.

Started from a cube for a flat base and tried to keep overhangs "reasonable" this time.

Started playing around with TopMod, the open source topological mesh modeler, after seeing a piece of art fabbed from a file it generated, in a blog post about fabbing and art.

Figured I'd start with something relatively simple and see how it rendered on Thingiverse.

Download it here: topmod3d.org/

Post here: gadgets.boingboing.net/2009/04/07/3d-printer-art-draft.html