# Mathematical “Sculptures”

This page illustrates a series of mathematical sculptures developed by Nicholas Mee, author of *Higgs Force*. There are 5 images on this page – I’ve deliberately separated them to allow you to enjoy each separately. I’ve also provided links to Nick’s website if you’re interested to find out more.

## The Kaleidoscope

We can construct a kaleidoscope out of three triangular mirrors that produces images with the symmetry of a polyhedron. The three mirrors are joined along their edges to form three of the four faces of a tetrahedron (not a regular tetrahedron). The kaleidoscopic image is then viewed through the open face of this tetrahedron. An example with icosahedral symmetry is shown above.

Scroll on down to see a very unusual honeycomb!

## The HoneyComb

If we add the fourth triangular mirror to complete the tetrahedron, we can construct kaleidoscopes that produce images with the same symmetry as space filling combinations of polyhedra, which are known as honeycombs. The above illustration was produced with this type of virtual kaleidoscope, with the camera positioned inside the virtual tetrahedron. It shows a honeycomb of octahedra and cuboctahedra.

Next up: A Torus Knot

## A Torus Knot

This beautiful structure is a torus knot from the Virtual Image CD-ROM *Art and Mathematics*. Sometimes it’s hard to forget that these scultures aren’t physical artifacts, but are simply made from 1’s and 0’s with a dash of mathematics!

And now for something pink and shiny…

## A Beaded Torus

A torus with a torus knot formed of golden beads wrapped around. The torus is the only compact two-dimensional Calabi-Yau manifold. This animation forms part of the Intersections: Henry Moore and Stringed Surfaces exhibition at the Royal Society.

And finally – something a bit more regular…

## A Compound Polyhedron

This image is a compound polyhedron formed from two regular dodecahedra. It was produced for the CD-ROM *POLYTOPIA I: Tessellations and Polyhedra*