Ed 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. . . . . . .
That's a cool demo! As an abstract regular polytope, the 57-cell has as its group of symmetries L(2,19), aka PSL(2,19). The lowest dimension of a permutation representation of this group is 20. So to embed the 2-skeleton of the 57-cell (171 dodecahedra suitably identified) in R^n so that its symmetries are all elements of O(n), we'd need n >= 20. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele