# 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*

{ 11 comments… read them below or add one }

I just want to say how much I am enjoying the revised edition of Higg’s Force by Nicholas Mee. As a scientific pygmy I have battled for some time to get a basic understanding of Particle Physics; something that completely enthrals me. His book is so well written that the basics are becoming much clearer to me. I envy those people who have the amazing intelligence to delve into the wonders of the universe and its components. Anyone who can simplify it for those of us who have the passion but not the ability or education, is greatly appreciated.

Regards Phil

The shapes of the structures are wonderful.

KoollooK !!

These virtual sculptures are aesthetically pleasing in themselves but to me are also a reminder of the precise geometry that underlies the apparent diversity of the world, (and beyond that cosmos), that we inhabit.

Beautiful Scultures. I particularly like the Torus knot.

Thank you.

They’re truly wonderful shapes – quite extraordinary!

I never get tired of trying, usually in vain, to understand these ideas.

Wonderful ! God is great.

Fabulous stuff, for guys like Phill (ab0ve) and me this is “otherworldly” and

the attmpt to understand “your world” of particle physics is made much

more interesting with every email. Keep up the great work. Best Regards, Dave

It is a joy to see math and electricity coalescing into such a splendiferous, animated art form.

I have no idea how the images are derived mathematically since I am a doctor and not a mathematician but they are truly splendid and mind boggling. Many thanks

Aesthetically beautiful and challenging.