The usual version of a Möbius strip has as its single boundary curve an unknotted loop. An unknotted loop can be deformed into a circle, with the strip deformed along with it.

In this version, the boundary of the strip is the circle in the middle, and the surface "goes through infinity", meaning that the grid pattern should extend outwards all the way. To save on costs, I've removed the grid lines that would require an infinite amount of plastic to print.

This was designed with Saul Schleimer.

treble clef pendant,
chainhole 5 mm

 I've always loved faceted structures, especially irregular ones that are becoming more and more common in architecture thanks to new technologies. They seem to have such complexity and they appear different from every angle you view them. Those are qualities I was looking for when I created the Faceted Cuff.

I designed the model for the Faceted Cuff much like it might be built if it were an actual structure. I began with a series of frames with the same number of varying points. Once these were arranged in the shape of a cuff I added interconnecting members, one by one. I kept the sizing of each member small enough so that it would give the appearance of a delicate structure that in reality was quite strong. The final result is 3D printed in White Strong & Flexible Polished so that it is smooth, lightweight, and of course strong and flexible.
The size as shown is SMALL, but you can also order it in X-Small and Medium (see links below). See the guide in the last photo for how these are measured: 

SMALL -
Inside dimensions 2 3/8" across, 1 3/4" in height
60mm across, 43mm in height 

X-SMALL
http://www.shapeways.com/model/277781/faceted_cuff_in_x_small.html?gid=ug

MEDIUM
http://www.shapeways.com/model/277755/faceted_cuff_in_size_medium.html?gid=ug



 

Just a note: I have only ordered this particular item in stainless steel. It came out great but I am not 100% on the other materials being printable

This is made by gluing two copies of the Round Möbius Strip along their boundaries. A Klein bottle in 3-dimensional space has to intersect itself, and in this case it intersects itself along a straight line. This was designed with the assistance of Saul Schleimer.

The 120-cell is one of the six regular 4-dimensional polytopes, the 4-dimensional analogues of the 3-dimensional polyhedra. This is the result of taking the edges of the polytope, radially projecting them onto the unit 3-sphere in 4-dimensional space, then stereographically projecting the result into our 3-dimensional space. We remove the half of the design in the hemi-3-sphere nearest to the projection point, which makes printing the image in 3-dimensional space feasible. A smaller version is available at http://shpws.me/lpmV