On Oct 9, 2004, at 1:02 PM, Fredrik Jagenheim wrote: > Yes, you're not the only one confused. It would be great if there was > a solution given that one could use to compare the output from, > preferably from a simple case as 'given these coordinates, you should > get these coordinates.' I can give you that (below, with rounded values to preserve line wrapping) but the problem is that the order of faces, and points within those faces, can be specified in any order and still achieve the same end result. Still, when it comes time to actually verifying any solutions, some sort of structured format would be nice, so that I can read them in, plot them, and see if it looks right. :) Sample output for a tetrahedron of frequency 0: [ [ -0.816, -0.471, -0.333 ], [ 0.000, 0.943, -0.333 ], [ 0.816, -0.471, -0.333 ] ] [ [ -0.816, -0.471, -0.333 ], [ 0.816, -0.471, -0.333 ], [ 0.000, 0.000, 1.000 ] ] [ [ -0.816, -0.471, -0.333 ], [ 0.000, 0.000, 1.000 ], [ 0.000, 0.943, -0.333 ] ] [ [ 0.000, 0.000, 1.000 ], [ 0.816, -0.471, -0.333 ], [ 0.000, 0.943, -0.333 ] ] Sample output for an octahedron of frequency 1: [ [ 0.000, -0.707, 0.707 ], [ 0.707, 0.000, 0.707 ], [ 0.000, 0.000, 1.000 ] ] [ [ 0.000, -0.707, 0.707 ], [ 0.000, -1.000, 0.000 ], [ 0.707, -0.707, 0.000 ] ] [ [ 0.707, 0.000, 0.707 ], [ 0.000, -0.707, 0.707 ], [ 0.707, -0.707, 0.000 ] ] [ [ 1.000, 0.000, 0.000 ], [ 0.707, 0.000, 0.707 ], [ 0.707, -0.707, 0.000 ] ] [ [ -0.707, 0.000, 0.707 ], [ 0.000, -0.707, 0.707 ], [ 0.000, 0.000, 1.000 ] ] [ [ -0.707, 0.000, 0.707 ], [ -1.000, 0.000, 0.000 ], [ -0.707, -0.707, 0.000 ] ] [ [ 0.000, -0.707, 0.707 ], [ -0.707, 0.000, 0.707 ], [ -0.707, -0.707, 0.000 ] ] [ [ 0.000, -1.000, 0.000 ], [ 0.000, -0.707, 0.707 ], [ -0.707, -0.707, 0.000 ] ] [ [ 0.000, 0.707, 0.707 ], [ -0.707, 0.000, 0.707 ], [ 0.000, 0.000, 1.000 ] ] [ [ 0.000, 0.707, 0.707 ], [ 0.000, 1.000, 0.000 ], [ -0.707, 0.707, 0.000 ] ] [ [ -0.707, 0.000, 0.707 ], [ 0.000, 0.707, 0.707 ], [ -0.707, 0.707, 0.000 ] ] [ [ -1.000, 0.000, 0.000 ], [ -0.707, 0.000, 0.707 ], [ -0.707, 0.707, 0.000 ] ] [ [ 0.707, 0.000, 0.707 ], [ 0.000, 0.707, 0.707 ], [ 0.000, 0.000, 1.000 ] ] [ [ 0.707, 0.000, 0.707 ], [ 1.000, 0.000, 0.000 ], [ 0.707, 0.707, 0.000 ] ] [ [ 0.000, 0.707, 0.707 ], [ 0.707, 0.000, 0.707 ], [ 0.707, 0.707, 0.000 ] ] [ [ 0.000, 1.000, 0.000 ], [ 0.000, 0.707, 0.707 ], [ 0.707, 0.707, 0.000 ] ] [ [ -0.707, 0.000, -0.707 ], [ 0.000, 0.707, -0.707 ], [ 0.000, 0.000, -1.000 ] ] [ [ -0.707, 0.000, -0.707 ], [ -1.000, 0.000, 0.000 ], [ -0.707, 0.707, 0.000 ] ] [ [ 0.000, 0.707, -0.707 ], [ -0.707, 0.000, -0.707 ], [ -0.707, 0.707, 0.000 ] ] [ [ 0.000, 1.000, 0.000 ], [ 0.000, 0.707, -0.707 ], [ -0.707, 0.707, 0.000 ] ] [ [ 0.000, 0.707, -0.707 ], [ 0.707, 0.000, -0.707 ], [ 0.000, 0.000, -1.000 ] ] [ [ 0.000, 0.707, -0.707 ], [ 0.000, 1.000, 0.000 ], [ 0.707, 0.707, 0.000 ] ] [ [ 0.707, 0.000, -0.707 ], [ 0.000, 0.707, -0.707 ], [ 0.707, 0.707, 0.000 ] ] [ [ 1.000, 0.000, 0.000 ], [ 0.707, 0.000, -0.707 ], [ 0.707, 0.707, 0.000 ] ] [ [ 0.707, 0.000, -0.707 ], [ 0.000, -0.707, -0.707 ], [ 0.000, 0.000, -1.000 ] ] [ [ 0.707, 0.000, -0.707 ], [ 1.000, 0.000, 0.000 ], [ 0.707, -0.707, 0.000 ] ] [ [ 0.000, -0.707, -0.707 ], [ 0.707, 0.000, -0.707 ], [ 0.707, -0.707, 0.000 ] ] [ [ 0.000, -1.000, 0.000 ], [ 0.000, -0.707, -0.707 ], [ 0.707, -0.707, 0.000 ] ] [ [ 0.000, -0.707, -0.707 ], [ -0.707, 0.000, -0.707 ], [ 0.000, 0.000, -1.000 ] ] [ [ 0.000, -0.707, -0.707 ], [ 0.000, -1.000, 0.000 ], [ -0.707, -0.707, 0.000 ] ] [ [ -0.707, 0.000, -0.707 ], [ 0.000, -0.707, -0.707 ], [ -0.707, -0.707, 0.000 ] ] [ [ -1.000, 0.000, 0.000 ], [ -0.707, 0.000, -0.707 ], [ -0.707, -0.707, 0.000 ] ] Sample output for a tetrahedron of frequency 2: [ [ 0.426, -0.739, -0.522 ], [ 0.853, 0.000, -0.522 ], [ 0.816, -0.471, -0.333 ] ] [ [ 0.426, 0.739, -0.522 ], [ -0.426, 0.739, -0.522 ], [ 0.000, 0.943, -0.333 ] ] [ [ -0.426, 0.739, -0.522 ], [ 0.426, 0.739, -0.522 ], [ 0.000, 0.000, -1.000 ] ] [ [ -0.853, 0.000, -0.522 ], [ -0.426, 0.739, -0.522 ], [ 0.000, 0.000, -1.000 ] ] [ [ -0.426, -0.739, -0.522 ], [ -0.853, 0.000, -0.522 ], [ 0.000, 0.000, -1.000 ] ] [ [ 0.426, -0.739, -0.522 ], [ -0.426, -0.739, -0.522 ], [ 0.000, 0.000, -1.000 ] ] [ [ 0.853, 0.000, -0.522 ], [ 0.426, -0.739, -0.522 ], [ 0.000, 0.000, -1.000 ] ] [ [ 0.426, 0.739, -0.522 ], [ 0.853, 0.000, -0.522 ], [ 0.000, 0.000, -1.000 ] ] [ [ -0.853, 0.000, -0.522 ], [ -0.426, -0.739, -0.522 ], [ -0.816, -0.471, -0.333 ] ] [ [ -0.426, -0.246, 0.870 ], [ 0.426, -0.246, 0.870 ], [ 0.000, 0.000, 1.000 ] ] [ [ 0.853, -0.492, 0.174 ], [ 0.426, -0.739, -0.522 ], [ 0.816, -0.471, -0.333 ] ] [ [ 0.426, -0.739, -0.522 ], [ 0.853, -0.492, 0.174 ], [ 0.000, -0.943, 0.333 ] ] [ [ -0.426, -0.739, -0.522 ], [ 0.426, -0.739, -0.522 ], [ 0.000, -0.943, 0.333 ] ] [ [ -0.853, -0.492, 0.174 ], [ -0.426, -0.739, -0.522 ], [ 0.000, -0.943, 0.333 ] ] [ [ -0.426, -0.246, 0.870 ], [ -0.853, -0.492, 0.174 ], [ 0.000, -0.943, 0.333 ] ] [ [ 0.426, -0.246, 0.870 ], [ -0.426, -0.246, 0.870 ], [ 0.000, -0.943, 0.333 ] ] [ [ 0.853, -0.492, 0.174 ], [ 0.426, -0.246, 0.870 ], [ 0.000, -0.943, 0.333 ] ] [ [ -0.426, -0.739, -0.522 ], [ -0.853, -0.492, 0.174 ], [ -0.816, -0.471, -0.333 ] ] [ [ -0.426, 0.739, -0.522 ], [ 0.000, 0.985, 0.174 ], [ 0.000, 0.943, -0.333 ] ] [ [ 0.000, 0.492, 0.870 ], [ -0.426, -0.246, 0.870 ], [ 0.000, 0.000, 1.000 ] ] [ [ -0.426, -0.246, 0.870 ], [ 0.000, 0.492, 0.870 ], [ -0.816, 0.471, 0.333 ] ] [ [ -0.853, -0.492, 0.174 ], [ -0.426, -0.246, 0.870 ], [ -0.816, 0.471, 0.333 ] ] [ [ -0.853, 0.000, -0.522 ], [ -0.853, -0.492, 0.174 ], [ -0.816, 0.471, 0.333 ] ] [ [ -0.426, 0.739, -0.522 ], [ -0.853, 0.000, -0.522 ], [ -0.816, 0.471, 0.333 ] ] [ [ 0.000, 0.985, 0.174 ], [ -0.426, 0.739, -0.522 ], [ -0.816, 0.471, 0.333 ] ] [ [ 0.000, 0.492, 0.870 ], [ 0.000, 0.985, 0.174 ], [ -0.816, 0.471, 0.333 ] ] [ [ -0.853, -0.492, 0.174 ], [ -0.853, 0.000, -0.522 ], [ -0.816, -0.471, -0.333 ] ] [ [ 0.000, 0.985, 0.174 ], [ 0.426, 0.739, -0.522 ], [ 0.000, 0.943, -0.333 ] ] [ [ 0.853, 0.000, -0.522 ], [ 0.853, -0.492, 0.174 ], [ 0.816, -0.471, -0.333 ] ] [ [ 0.853, -0.492, 0.174 ], [ 0.853, 0.000, -0.522 ], [ 0.816, 0.471, 0.333 ] ] [ [ 0.426, -0.246, 0.870 ], [ 0.853, -0.492, 0.174 ], [ 0.816, 0.471, 0.333 ] ] [ [ 0.000, 0.492, 0.870 ], [ 0.426, -0.246, 0.870 ], [ 0.816, 0.471, 0.333 ] ] [ [ 0.000, 0.985, 0.174 ], [ 0.000, 0.492, 0.870 ], [ 0.816, 0.471, 0.333 ] ] [ [ 0.426, 0.739, -0.522 ], [ 0.000, 0.985, 0.174 ], [ 0.816, 0.471, 0.333 ] ] [ [ 0.853, 0.000, -0.522 ], [ 0.426, 0.739, -0.522 ], [ 0.816, 0.471, 0.333 ] ] [ [ 0.426, -0.246, 0.870 ], [ 0.000, 0.492, 0.870 ], [ 0.000, 0.000, 1.000 ] ] Sample output for an icosahedron of frequency 3: [ [ 0.443, 0.864, 0.239 ], [ 0.682, 0.717, 0.148 ], [ 0.526, 0.851, 0.000 ] ] [ [ 0.717, 0.148, 0.682 ], [ 0.851, 0.000, 0.526 ], [ 0.864, 0.239, 0.443 ] ] [ [ 0.688, 0.425, 0.588 ], [ 0.717, 0.148, 0.682 ], [ 0.864, 0.239, 0.443 ] ] [ [ 0.809, 0.500, 0.309 ], [ 0.688, 0.425, 0.588 ], [ 0.864, 0.239, 0.443 ] ] [ [ 0.688, 0.425, 0.588 ], [ 0.809, 0.500, 0.309 ], [ 0.588, 0.688, 0.425 ] ] [ [ 0.425, 0.588, 0.688 ], [ 0.688, 0.425, 0.588 ], [ 0.588, 0.688, 0.425 ] ] [ [ 0.309, 0.809, 0.500 ], [ 0.425, 0.588, 0.688 ], [ 0.588, 0.688, 0.425 ] ] [ [ 0.443, 0.864, 0.239 ], [ 0.309, 0.809, 0.500 ], [ 0.588, 0.688, 0.425 ] ] [ [ 0.682, 0.717, 0.148 ], [ 0.443, 0.864, 0.239 ], [ 0.588, 0.688, 0.425 ] ] [ [ 0.809, 0.500, 0.309 ], [ 0.682, 0.717, 0.148 ], [ 0.588, 0.688, 0.425 ] ] [ [ 0.425, 0.588, 0.688 ], [ 0.239, 0.443, 0.864 ], [ 0.500, 0.309, 0.809 ] ] [ [ 0.688, 0.425, 0.588 ], [ 0.425, 0.588, 0.688 ], [ 0.500, 0.309, 0.809 ] ] [ [ 0.717, 0.148, 0.682 ], [ 0.688, 0.425, 0.588 ], [ 0.500, 0.309, 0.809 ] ] [ [ 0.239, 0.443, 0.864 ], [ 0.425, 0.588, 0.688 ], [ 0.148, 0.682, 0.717 ] ] [ [ 0.000, 0.526, 0.851 ], [ 0.239, 0.443, 0.864 ], [ 0.148, 0.682, 0.717 ] ] [ [ 0.425, 0.588, 0.688 ], [ 0.309, 0.809, 0.500 ], [ 0.148, 0.682, 0.717 ] ] [ [ -0.443, 0.864, 0.239 ], [ -0.295, 0.955, 0.000 ], [ -0.526, 0.851, 0.000 ] ] [ [ 0.443, 0.864, 0.239 ], [ 0.526, 0.851, 0.000 ], [ 0.295, 0.955, 0.000 ] ] [ [ 0.162, 0.951, 0.263 ], [ 0.443, 0.864, 0.239 ], [ 0.295, 0.955, 0.000 ] ] [ [ 0.000, 1.000, 0.000 ], [ 0.162, 0.951, 0.263 ], [ 0.295, 0.955, 0.000 ] ] [ [ 0.162, 0.951, 0.263 ], [ 0.000, 1.000, 0.000 ], [ -0.162, 0.951, 0.263 ] ] [ [ 0.000, 0.851, 0.526 ], [ 0.162, 0.951, 0.263 ], [ -0.162, 0.951, 0.263 ] ] [ [ -0.309, 0.809, 0.500 ], [ 0.000, 0.851, 0.526 ], [ -0.162, 0.951, 0.263 ] ] [ [ -0.443, 0.864, 0.239 ], [ -0.309, 0.809, 0.500 ], [ -0.162, 0.951, 0.263 ] ] [ [ -0.295, 0.955, 0.000 ], [ -0.443, 0.864, 0.239 ], [ -0.162, 0.951, 0.263 ] ] [ [ 0.000, 1.000, 0.000 ], [ -0.295, 0.955, 0.000 ], [ -0.162, 0.951, 0.263 ] ] [ [ 0.000, 0.851, 0.526 ], [ 0.148, 0.682, 0.717 ], [ 0.309, 0.809, 0.500 ] ] [ [ 0.162, 0.951, 0.263 ], [ 0.000, 0.851, 0.526 ], [ 0.309, 0.809, 0.500 ] ] [ [ 0.443, 0.864, 0.239 ], [ 0.162, 0.951, 0.263 ], [ 0.309, 0.809, 0.500 ] ] [ [ 0.148, 0.682, 0.717 ], [ 0.000, 0.851, 0.526 ], [ -0.148, 0.682, 0.717 ] ] [ [ 0.000, 0.526, 0.851 ], [ 0.148, 0.682, 0.717 ], [ -0.148, 0.682, 0.717 ] ] [ [ 0.000, 0.851, 0.526 ], [ -0.309, 0.809, 0.500 ], [ -0.148, 0.682, 0.717 ] ] [ [ -0.717, 0.148, 0.682 ], [ -0.864, 0.239, 0.443 ], [ -0.851, 0.000, 0.526 ] ] [ [ -0.443, 0.864, 0.239 ], [ -0.526, 0.851, 0.000 ], [ -0.682, 0.717, 0.148 ] ] [ [ -0.588, 0.688, 0.425 ], [ -0.443, 0.864, 0.239 ], [ -0.682, 0.717, 0.148 ] ] [ [ -0.809, 0.500, 0.309 ], [ -0.588, 0.688, 0.425 ], [ -0.682, 0.717, 0.148 ] ] [ [ -0.588, 0.688, 0.425 ], [ -0.809, 0.500, 0.309 ], [ -0.688, 0.425, 0.588 ] ] [ [ -0.425, 0.588, 0.688 ], [ -0.588, 0.688, 0.425 ], [ -0.688, 0.425, 0.588 ] ] [ [ -0.500, 0.309, 0.809 ], [ -0.425, 0.588, 0.688 ], [ -0.688, 0.425, 0.588 ] ] [ [ -0.717, 0.148, 0.682 ], [ -0.500, 0.309, 0.809 ], [ -0.688, 0.425, 0.588 ] ] ...truncated... -- (-, /\ \/ / /\/