Check out gibell's Reuleaux solids at http://www.shapeways.com/model/115463/reuleaux_solids_3cm.html Those are surfaces of rotation based on Reuleaux polygons, which are curves of constant width. These are also surfaces of constant width, but *not* surfaces of rotation. So despite looking decidedly non-spherical, they roll smoothly as spheres.

There are two different Meissner solids, subtly different.  Look closely at the edges.  Some are rounded and some are sharp.  One of them has the round edges making a a triangle and the sharp edges meeting at a point; the other has them the other way around.

These are sized for compatibility with gibell's solids, so if you get all five they will all roll smoothly under the same flat surface together.  And like gibell's, they are hollow with internal braces to lend extra support, with holes in the bottom to let the support material out.

Printed great.  Video below! (the two foreground shapes are mine; the red one in the background is one of gibell's from the set linked above)

A set of FIVE dice in this item: d4, d6, d8, d12, d20. Each die is realized by a "skeleton" (See Sylook''s shop at http://www.shapeways.com/shops/the_shop_of_small_wonders for the idea behind it), with a wireframe model of the *dual* of the relevant polyhedron surrounding the skeleton. The numerals are affixed to the wireframe, which is free to move around on the skeleton--but not too far. Hence the name "rattling bones." (The d4 is a little different; the numbers are on the ends of the skeleton)

So far, has been canceled in steel (antique bronze glossy. reason: Loose parts can't be kept loose without breaking) and in Alumide (reason: Thin wall,
(Probably will be impossible to clean in detail material. I don't know about glass, but I think these really have to be done in strong&flexible.)

A d12 that''s a *rhombic* dodecahedron instead of a regular one.

This die is a shell surrounding a chunk of the support material, for cost purposes. It's 3cm in radius, which turns out to be a nice solid size for a die. The numbers look big enough to be readable, and it very decisively lands on a single face with a single face up. A handsome piece of random-number generation!

There's a 4cm version of this too, but I'm starting to think that might be overkill.

A single die that emulates all the possible rolls of two six-sided dice. All 36 possible rolls are depicted on its 36 faces, using die-pip diagrams. It should be big enough to read, since it''s nice and roomy and hollow.

The pips are maybe a little too deep, but otherwise pretty good.

In the “Fudge” gaming system, one commonly rolls four dice, each numbered with “+”, “-”, and “0”.  Since those are d3, and 2d3 are equivalent to a d9, you can emulate a Fudge roll with two of these dice (each one substituting for 2d3) without changing the odds.

I'm not sure about the numbering for this die.  Using “++” and “--” didn't look so good for the double-plus/minus points, but “+1”/“-1” didn't look so good on the single-plus/minus spots.  So there's sort of a hybrid notation here: one face reads “+2”, and one reads “-2”, then there are two labeled “+” and two labeled “-”, and then three labeled “0”, in order to emulate the odds of 2dF properly.  The single “+” and “-” signs are designed to look different from one another even in bad printing (but the proof will be in the actual printing).

The die is hollow, for minimal volume and smaller rotational inertia, and also has thinner curved sections than my other d9s, so hopefully should not roll too long.

The rarely-seen forty-eight-sided die! Yes, forty-eight adventure-loving faces, waiting to generate random numbers for you.

The edges are raised, and so are the numbers (but not as much as the edges).

Printed out pretty nicely! The digits are small, but readable.

Like the regular d9, but hollow. So maybe it won't roll as long.

The rhombic hexecontahedron is a pretty shape; it's used as the symbol for Wolfram Alpha. It's also non-convex, so it can't be used as a die... or can it? Since it's a facetting of the regular dodecahedron, it essentially lands on five vertices which are the corners of one face of the enclosing regular dodecahedron. So with a little creative labelling, it can certainly be used as an ordinary d12.

As usual, order at your own risk until I've put up pictures of the actual print.

OK, got my print of this, and I have to say that as it stands, it's something of a failure. The points are so sharp and fine that the colors actually "bleed" across to other faces a little, here and there. And the numbers are too bold and dark and tend to look like big black blobs. Besides, the points are too pointy for using as a die. There are good uses for full-color sandstone: this isn't one of them. Maybe I can redesign.

Spherical d12 with an icosahedron-shaped hollow inside and a ball rolling around in it, so it should land with a number upward.

Added some extra pieces to hold the centers of the 4, 6, 8, 9, 0 in place.

Print was okay, though the centers of the 8 fell out. Doesn't quite always land face-up, still working on it.

Might be cool in Frosted Detail, with the transparency and the liquid support material.

The d4 of the "Open" series. Labeling the faces of a d4 doesn''t make as much sense, so the tilted faces now reside under the vertices.

(Compare this with the "Tetrasphere" by friz at http://www.shapeways.com/model/152256/tetrasphere.html which is similar)

The d20 in the "Open" series. Doing a true rotated triangle in these would have left the triangle really small, so I went with more of a hexagon to suggest the right shape.

cunso namcu bliku .i lo sefta cu se tcita zo pa bi''o zo gai

6-sided dice that bear a strange combination of numbers, but still have exactly the same odds for every total as an ordinary pair of d6s. See http://en.wikipedia.org/wiki/Sicherman_dice

They have an empty pocket inside, full of support material, to lower price.

(general advice: dice look good in detail material)

I''ve seen d30s with the English alphabet on them (and four "wildcards" or something). So I figured I''d do a similar one with the Hebrew alphabet. The Hebrew alphabet only has 22 letters, and I also included the five special final forms (and three starred faces to take up the rest).

Letters are indeed used as numbers in Hebrew... but not this way. This is an alphabet teaching tool.

(Hollow, filled with support material)

A sphere with a cubical hollow inside, in which a ball rolls, so it will land with one of eight "faces" up. Pipped.

Arrived still stuffed with support material (powder). Poked an unbent paperclip into the pips to help clear it out, blew in air, bounced on table, etc. Note: White, Strong, and Flexible is also quite bouncy!

A pipped d6 in the "open" theme, with the raised pips on tilted squares inside a cubical framework.

Customize this die! Send me 1-6 black-and-white drawings (or numbers/words/symbols) to be embossed on the sides of the die, and I''ll put them on for you.

IF YOU WANT TO CUSTOMIZE THIS DIE:

Each side can have EITHER text (up to 3 characters, unicode accepted if I have a font for it) or a graphic symbol on it. If you upload pictures, please make sure they consist of ONLY black and white pixels (no color or grayscale); black will be the foreground (raised). Keep in mind that the drawing area is a square about 11mm on a side, and the resolution of 3D printing is limited. Your picture will be raised 0.7mm above the background (putting it 0.3mm below the level of the outer cube face).

If you provide text, I'll choose a suitable font for it; for complete control over the look make pictures instead. Any faces with no text or image provided will be supplied with pips, or left blank (please tell me which you prefer in the comments)

A complete set of the "open" dice: a d4, d6, d8, d20 and two d12s (one normal and one rhombic).

Placed together here, this shows a mistake in my design process: I did not consider the scale of the dice next to each other. Oops.

Ever roll a die and just KNOW the answer in advance? This die is a foregone conclusion. It''s based on the unistable polyhedron from http://mathworld.wolfram.com/UnistablePolyhedron.html ; if I did things right it should ONLY be able to land on one face (the opposite edge is helpfully marked with a single split pip)

(General advice: dice look good in detail material)

Print has come back and this die does NOT work as advertised! It seems to have more than one place it can come to rest. Back to the drawing board.

I think the problem lieth with the light weight of the material and the surface ridges that detail material has from the printing process (my sample was printed in black detail). Trying one with much shallower slanted sides, so the weight of the wider bottom is more significant.

Have to find a good size. This is a solid version.

This one is way too small. The numbers are unreadable.

(Get one of the hollow versions I have; I'm keeping this model around only because of all the comments on it.)

A small, plain sphericon. It's a wee little thing, maybe the size of a marble, and it rolls in a straight line like one too, but not in a straight line (a sphere or cylinder can roll straight. A cone rolls around in tight circles. A sphericon wobbles, rolling in alternating half-circles as its cone faces take turns, and so follows a more or less straight path by wobbling back and forth)

Another in the "open" series, the numbers are on small triangles inside the larger "cage."

Johannes Kepler thought he had hit upon a secret of the universe, a demonstration of the guiding hand of God (and geometry) in the structure of the heavens. In his _Mysterium Cosmographicum_ (see http://en.wikipedia.com/wiki/Johannes_Kepler#Mysterium_Cosmographicum), he showed how the (circular) orbits of the planets could be shown to correspond to the five Platonic regular solids, nested inside and outside the spheres containing the orbits. It's an elegant theory, consonant with the idea of perfection in the heavens, and even explains why there were only six planets (because there are only five convex regular solids).

Of course, for all its beauty and elegance, the theory is *wrong*, and indeed there is no relationship between the Platonic solids and the orbits of the planets, and the planets don't even move in circles, and there are more than six of them. Still, here is a model of Kepler's original idea, rendered in thin wires. The spheres of the planets' orbits are suggested by half-spheres of eight spokes, and the solids are rendered in wireframe nesting within them. Because of the thickness of the wires, the solids and the spheres overlap a little—a feature which, I hope, keeps the model together. There are also some support wires, two running across the top of the spheres and one down through their pole.

An initial print has proved... not as bad as might be. The thin "wires" of WSF material are somewhat too flexible for the project, but only on the outermost shapes (the outermost sphere and especially the cube). The inner ones, even the tetrahedron, are fairly sturdy and rigid enough. I've thickened the wires of the cube and also added an "X" of supporting struts on each face of the cube and attached them to the next smaller sphere, and a "Y" of them on each face of the tetrahedron for good measure. I also put two more rings on the outermost sphere for more stability and added a base so that it has something to stand on. Might still be a little wobbly, but everything added makes it more expensive, so I'm hoping to do more with less. Have not yet printed the new version.

Not a reasonable die, but hey, Rhombic Hexecontahedron don''t need no reason.

Very cool-looking, but also very sharp at the corners! Be careful.

Boy Surface, in my favorite projection. It's in a network form, partly to cut down on volume but also because the whole point is to be able to see the internal structure.

Doubling cube? Up to 64 isn't high enough! OK, you don't really roll a doubling cube, and so it starts from 2 instead of 1, and so on. But anyway, this is a crystal-shaped d16 doubling die, numbered from 1 up to a whopping 32,768!

First attempt at a dreidel, ordinary Hebrew letters, etc.