# Symmetries

Ned and I decided to do an art project that might be called virtual sculpture with mirrors. We took three mirrors, positioned at right angles, as you can see in the picture, viewed from the back (you can see where the mirrors are taped together). This arrangement of mirrors makes it look like there are eight of anything you put in front. That’s because each mirror doubles things (the thing itself plus its reflection) so you get 2 × 2 × 2 of everything, which is eight.

Then we positioned four shapes, each made from clear plastic tubing. The idea was to make shapes that, when placed against the mirror, would create the edges of cool looking virtual regular and semi-regular solids. Below are the four shapes we placed against the mirrors.

Here you see all the shapes together in front of the three mirrors, held together by blue tape. It really does look like a fully rounded object, doesn’t it? We didn’t like the way the blue tape looked, so we redid it all a little more carefully.

Here is the final result, first seen from the side, so that the shapes look almost fully round…

and then finally fully from the front. We lit the whole thing with a spotlight, so it would glow in a really wonderful eery way. Unfortunately the glow was so bright that it burns out the image on the digital camera, so you can’t see all the details in the actual sculpture.

The four nested virtual sculptures are, listing from inside to out, an octahedron, a cube, a cubeoctahedron and a rhombic icosahedron. In the second photo above (the one that shows the inserts lying flat on a blue surface), the corresponding inserts are arranged from bottom to top.

This, in case you were wondering, is what people do when they live in the woods around Santa Cruz. Now you know.