Where are they?

If you know your 3-D regular solids, you'll have noticed that hexagons seem in short supply. But the Hall of Hexagons can show you where to find them...

You'll need a Java enabled browser for the 3-D stuff - Microsoft can't make any money out of Java and they make life difficult for you by not including it in their browser - however you should get a simple prompt for the download if necessary. The 3-D realisations are done with the LiveGraphics3D applet - which is a very fine piece of work. If you see an odd glitch, it's probably due to the applet's sensible compromise between speed and accurate realisation - blame it on me, because the models are hand-coded (without Mathematica); if I had time I could program around it.

How to play with the LiveGraphics3D 3-D models:
In short, just drag the model with your mouse and rotate it. But if you want the full monty...:

* drag with the left mouse button pressed: model rotates about an axis intuitively
* release left mouse button while dragging: model carries on spinning
* SHIFT key pressed plus drag up/down: changes the zoom
* SHIFT key pressed plus drag left/right: model rotates clockwise/anticlockwise
* drag up/down with right mouse button (or META/ALT key) pressed: parts of the model are removed
* HOME key: restores the original picture

Platonic solids

We'll look firstly at the Platonic solids. A Platonic solid is a polyhedron whose faces are all regular polygons of the same size, with the same number of faces meeting at every vertex. Plato knew about them, which presumably explains the name. There are just five:

• the cube
• the dodecahedron
• the icosahedron
• the octahedron
• the tetrahedron

For more information on Platonic Solids try MathWorld or Wikipedia

Archimedean solids

An Archimedean solid has at least 2 different types of regular polygons as faces, with all vertices being 'identical' - ie if someone rotates an unmarked Archimedean solid, when you aren't looking, you can't tell which vertex was moved where.

There are 13 of them. The following are interesting from a hexagonal viewpoint:

• the truncated tetrahedron
• the truncated octahedron
• the truncated icosahedron
• the great rhombicosidodecahedron
• the cubeoctahedron

For more information on Archimedean Solids try MathWorld or Wikipedia

Prisms and antiprisms

These actually conform to the above definition of 'Archimedean solid', but they are traditionally categorised separately, because there are infinitely many of them. Here we have:

• the hexagonal prism and antiprism

page date: 18Nov04.      I enjoy correspondence stimulated by this site. You can contact me here.