Sliding Puzzles and precision laser cutting

I recently met David Litwin at Techshop on a couple of occasions. He is doing work on the lasercutter at a level of complexity and precision that surpasses anything else I've seen.

David has put together a triangular sliding puzzle composed of dozens of laser-cut parts. In order to make the sliding mechanism functional and easy to use, he has employed numerous innovations. For example, he created a laser cut acrylic notch-and-lever system that allows the rows of triangles to snap into the correct places as you slide them. He also laser-engraved countersinks for the screws he used to hold the layers together.





Due to his precision work, he has run into maddening calibration errors that most of us don't have to worry about. Any unevenness in the laser cutter's performance can screw up the precision sliding of the puzzle pieces.

You can read more about his design process on Twisty Puzzles.

Mirrored polyhedra

Laser cutters can engrave the back and front of glass and acrylic mirrors. They can cut acrylic mirrors.

A long time ago (2001), I experimented with creating mirror boxes -- 3D shapes where every face had a mirror surface on the inside. Thus, you could peer in and see an infinitely reflected image on the inside.

With the laser cutter, I could much more easily try more unusual shapes. Here's what I created with some quick experimentation:

This is a mirrored tetrahedron with laser-etched designs on the sides and light shining through:


This one is another tetrahedron that lets three people look in, and everyone sees each others' eyeballs copied.


The tetrahedron shape does not tessellate 3-space, so the reflections end up being very fragmented. I wanted to find a shape (other than the boring cube, triangular prism, and hexagonal prism) that would perfectly tessellate 3-space so that its reflections would all be completely consistent. It turns out that one exists -- it's called the rhombic dodecahedron. (wikipedial details)


Here's the inside, lit by a camera flash.



And lit by EL wire. Unfortunately, the camera's limited depth of field doesn't let me easily capture distant objects.





So far what I've done is really simple. I want to play around with some more interesting artistic possibilities.

Hilbert curves

There's a type of space-filling fractal curve called a Hilbert curve. In its mathematical form, it's an infinitely long line that winds its way around a finite space like a square. Wikipedia entry

In my recent tradition of trying All Sorts of Stuff on a laser cutter, I thought it might be interesting to cut a (finite) Hilbert curve into a sheet of paper with a laser cutter. This is the sort of thing that would take several days with an X-acto knife.

Now I have a square of paper that is only about 6x6 inches in size, but if I pulled the ends of it apart as far as they will go, it would be about 20 ft long. I cut a second one and pulled it apart to drape around my room like a long string.




I'm playing around with other forms of it to see if I can make a mobile:

Basic test.