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Orthogonal projection or Hasse diagram?
The image labelled "orthogonal projection" doesn't seem to be an orthogonal projection of the 10-cube; it looks more like the Hasse diagram of the 10-cube's face lattice. Could somebody verify this?—Tetracube (talk) 00:24, 20 August 2008 (UTC)
- Did you know that this is linked to from WP:NTHINGS? Professor M. Fiendish 03:53, 23 August 2009 (UTC)
- Both graphics are "skew" orthogonal projections, flatting 10-dimensions down to 2 dimensions (computed as a dot product from an orthonormal basis). The left-to-right column projection actually was my first attempt to generate a symmetric Petrie polygon view, before the correct projections were created. In my attempt, I determined the Petric polygon, and picked a [u,v] basis with u direction determined by a sum of the petrie polygon vertices so it came out as one vertex on the left, opposite vertex right, and progressive vertex-edge-vertex distances came out as vertical columns. So it was accidental, but interesting, so I kept it and another guy converted the projection from PNG to SVG. I actually just worked out how to compute the correct [u,v] orthogonal basis, given N sequential vertices of a 2N Petrie polygon, testing now on hypercube family... Tom Ruen (talk) 04:16, 23 August 2009 (UTC)
- p.s. Interestingly this projection projected a cube without any overlapping vertices, while a Petrie polygon for a cube looks like a hexagon with two central vertices. User:Qef/Orthographic_hypercube_diagrams Tom Ruen (talk) 04:19, 23 August 2009 (UTC)