Richard, I hope you are not trying to add to the article! How were the trips? Richard

What connexion, if any, is there twixt the 57-cell & the Hoffman-Singleton graph ??? R.

On Wed, 8 Oct 2008, Ed Pegg Jr wrote:

...

I made a demo on the 57-cell.  I seem to be the first to notice that the skeleton is the Perkel graph.  http://demonstrations.wolfram.com/The57Cell/

I tried to build the 57-cell in 4D.  I thought I would start by finding a really nice hemi-dodecahedron, or Petersen graph.

These six faces work really well: {{{0,0,2,0},{-1,-1,-1,Sqrt[5]},{2,0,0,0}, {-1,1,1,Sqrt[5]}, {0,0,-2,0}}, {{0,0,2,0}, {1,1,-1,Sqrt[5]},  {-2,0,0,0},{1,-1,1,Sqrt[5]}, {0,0,-2,0}}, {{0,2,0,0}, {-1,-1,-1,Sqrt[5]},{0,0,2,0}, {1,1,-1,Sqrt[5]}, {0,-2,0,0}}, {{0,2,0,0}, {1,-1,1,Sqrt[5]},  {0,0,-2,0},{-1,1,1,Sqrt[5]}, {0,-2,0,0}}, {{2,0,0,0}, {-1,-1,-1,Sqrt[5]},{0,2,0,0}, {1,-1,1,Sqrt[5]}, {-2,0,0,0}}, {{2,0,0,0}, {-1,1,1,Sqrt[5]},  {0,-2,0,0},{1,1,-1,Sqrt[5]}, {-2,0,0,0}}}

Connected vertices are at distance 4. Non-connected vertices are at distance 2Sqrt[2]. Any two diagonals are at right angles to each other, through the origin.  All faces have a bizarre regularity.

Unfortunately, these warped faces don't reflect to create new points, so I couldn't figure out how to glue two of these weird faces together.

--Ed Pegg Jr _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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-- Richard Nowakowski Dept. Mathematics & Statistics Dalhousie University, Halifax NS, B3H 3J5 Canada Phone (902)-494-6635 FAX (902)-494-5130