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.