There are six regular convex polytopes in 4D, which are analogous to the five Platonic solids in 3D. This is the fifth, the hyperdodecahedron, a remarkably beautiful object brought to my attention by George Hart.

Here it's shown in a Schlegel diagram so you can see all 120 dodecahedral cells, though most are transformed by perspective: in this projection, the only regular dodecahedra are the biggest one on the outside and the tiniest one at the center.

A smaller model is here.

This steampunk style knotted cog was procedurally generated using 3-dimensional spherical geometry, then stereographically projected into our (mostly) Euclidean universe.

Other sizes:
www.shapeways.com/model/231026/knotted_cog__large_.html
www.shapeways.com/model/231045/knotted_cog.html
www.shapeways.com/model/277265/knotted_cog__smaller_.html
www.shapeways.com/model/232385/knotted_cog__small_.html

Here's a 36 inch (approx.) necklace made of 72 octahedron links. Each link is 5/8 inch by 3/8 inch (16mm x 9.5mm).

Also available:
An extra long 55-inch Octahedalink Necklace, with 120 octahedron links.
The super long 7-Foot Necklace, with 185 octahedron links.
And the 30-inch Octahedron Link Necklace with 36 larger, chunkier, clunkier octahedron links.

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Want to get a set?

(the 36-inch necklace and matching earrings)?

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Or the set of 3 necklaces?

(the 36-inch, 55-inch and 7-foot necklaces)?

+ +

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30-inch necklace consisting of 36 octahedron-shaped links. Each link is approximately 1.25 x 1 inch. A chunky, clunky fashion statement, to be sure!

Also available in a 36-inch necklace with 72 smaller octahedron links Octahedralink Necklace.
My complete line of jewelry is displayed here: Jewely - All

Necklace constructed from pin and barrel links, rotated 90 degrees at each link.

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