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)

This is the Multidodecahedron. A puzzle that has all the parts from the Megaminx, Pyraminx Crystal, Starminx, Master Pentultimate and Pentultimate and requires you to solve them simultaneously. This puzzle was initially suggested by Carl Hoff, who coined the name Multidodecahedron.

About ordering

To purchase a Multidodecahedron DIY kit, you should purchase this model and then must send me an email with your order number so I can give the necessary instructions to Shapeways. This kit comes with free stickers so please also include your mailing address so I can send them to you (note: I am currently not offering super stickers).
This puzzle comes as a kit which you will need to assemble yourself. You will need to provide M3 screws and optional springs and or washers. You can also contact me directly to purchase a fully assembled and stickered copy of this puzzle.

This shape works very nicely as a 12 sided die, providing an elegant alternative to the regular dodecahedron.

It's is a hexagonal dipyramid, an isohedron.

Note that this is a blank, so the faces will need to be numbered.  For more information on unique dice shapes, see http://loki3.com/poly/fair-dice.html.

An archimedean polyhedron.

N. 12 of the complete set counting 13 items.

The truncated icosidodecahedron has 62 faces (30 squares,
20 hexagons,
12 decagons), 180 edges and 120 vertices.

The Archimedean solids are bounded by two or more kinds of regular polygons, meeting at each vertex in the same identical way.

They were discovered by Archimedes in a now-lost work. In 1620 Johannes Kepler described them all and gave them the names still in use.

Here's a 3-inch model consisting of a set of twelve interconnecting, colored pentagons; the exploded, twisted faces of a dodecahedron. See more of my color models: Vertigo's Colored Polyhedra

This puzzle is made of 6 equal pieces which form a dodecahedron. The assembly is not so easy

The faces of a dodecahedron have been extruded and rotated, and the the entire structure was slightly spherized.

Trying some more designs for dice now. This is a regular wireframe dodecahedron with smaller, rotated pentagons inset in each face with the numbers on it (not high enough to protrude above the frame.)