I don't think there's much in it; I think I like the icosahedron due its very large amount of symmetry but cube and octahedron would be my second choices.

Is Flash bad for that sort of thing? Isn't that where it's useful?

Well, you know, proprietary closed platform, better to support open standards, yadda yadda. Also Flash applets always seem to eat a bigger proportion of my CPU than they should reasonably need to. OTOH, I can't deny that my Flash applets respond very smoothly and look very slick for minimal coding effort – especially compared to the Java ones on the MathWorld page, which have a low refresh rate and no antialiasing. (Flash gave me antialiasing for free, just by using its graphics APIs in the perfectly obvious way.)

Probably one of these days I should look into whatever all this newfangled stuff is that's supposed to be the open-standards alternative to Flash. Embedded SVG manipulated by Javascript, or something like that, isn't it?

"Embedded SVG manipulated by Javascript, or something like that, isn't it?"

Yup, <canvas> is the magic tag. Although as you say in practice Flash gives great results and can be created with free tools.

Depends what you mean by great results - for me the flash player segfaulted twice while trying to view these, and even when working it caused firefox to freeze for 30 seconds while opening.

Oh yeah, fair enough. I'd like a good free alternative if one arrives, but it still seems to work better than the alternatives for this sort of thing at the moment.

I nearly voted for two, but decided that, as solids, the icosahedron definitely just edges it. If you get to compare the unfolded versions too then the dodecahedron is pretty damned good though.

PS, I like the spinning effect on your apps, with the different speeds depending on how hard you tugged them!

Thank you! It wasn't a new idea of mine – the MathWorld ones do the same, though the response isn't as smooth and they stop moving as soon as the mouse pointer goes outside their containing box – but I was pleased with how it came out when I tried it.

Yes I like the net of the dodecahedron :)

It's the unfolded version of the dodecahedron that edges it over the icosahedron. It's just lovely.

I actually have quite a definite favourite, and I'm pleased to see it's the most popular choice. :-)

No love for the cube, though - what's with that?

Cubes are great - perhaps it's got a face best for radio ;)

I love cubes, especially rubiks ones :) But they're more useful that beautiful.

Come to think of it, I have the word 'Cube' in my extended job title! So perhaps I should have voted for our six-faced friends.

When I was very young I played a Hunt The Wumpus implementation on the PET where the locations were connected like the vertices of a dodecahedron - explicitly described as such. My father introduced me to topology by pointing out you could draw the map in a convenient flat shape and it worked the same way.

Nowadays, of course, I think of it as a d12.

In this 1976 article the original Wumpus author says he chose the dodecahedron precisely because it was his favourite platonic solid...

Coo. I had no idea the non-regular maps came later.

I also admire the simplicity of the tetrahedron. Dodecahedrons are just vulgar.

So are you going to reveal what you and Drswirly think? Tell all!

As I commented to Simon on Mono last month:

• The tetrahedron is too dull. I mean, self-dual? What's the point of that?
  
• The cube is very functional and useful, but not really exciting.
  
• The icosahedron is a bit too busy, and like a sphere having a bad day.
  
• The dodecahedron is just showing off. Really, pentagons? Smug thing.
  

The octahedron is pleasantly surprising. It look all wide and square when you look at it with a vertex towards you, then tall and thin when with an edge towards you. And when placed flat on a table, it taunts and teases with its antiprismness, the cheeky little thing.

Your d12 no longer cries itself to sleep (http://www.cafepress.co.uk/orderofthestick.38652761)!