Hi folks. I realise that this subject is perhaps *a little* off topic, but I'm posting it here in case anyone else is interested. Jim's talking about the 4th dimension got me thinking... I want to do projections and slices of 4D shapes. But I don't have the software... A while back I managed to write a program to do wireframe projections of 4D figures. It wasn't all that good really! So I sat down and wondered if I could adapt my raytracer to draw 3D slices... But today I managed to get good old POV-Ray to draw it for me! Just took a bit of algebra shifting! A hypercube is the intersection of 8 hyperplanes. Each one is given by ax + by + cz + dw - e <= 0. To convert these into standard POVRay planes (ax + by + cz - f <= 0), just select a value for W, then f = dW + e. Now do a CSG intersection of all 8 planes and bob's your uncle! (Actually my uncle's name is John, but hey...) As I type this I'm doing some animations of various slices. This is where I need some help... I can get the slices to look like ordinary cubes (which vanish/appear at certain W values), but that's not vary exciting. If you cut a normal cube across a corner, you get a triangular section (rather than square). I managed to get a prism-shaped cross section out of my hypercube (by doing a 45 degree YW rotation), but how do I rotate the hypercube so that one of its corners faces along the W axis? (The hypercube starts out aligned to the coordinate axies.) Secondly, what other interesting 4D polyhedrons (?!) are there, and how do I construct them? Thanks folks! Andrew. PS. I say again, if anyone wants to see the POVRay files or just chat about the math, feel free to email me off list (or on list if enough people are interested...) PPS. I'd love to post pictures, but A) no binaries on a mailing list, and B) the animations are a tad TOO BIG to be emailing around anyway! _________________________________________________________________ Send and receive Hotmail on your mobile device: http://mobile.msn.com