vertex set invariant under sigma: True  under iota: True
edge set = all unit-distance pairs of V (induced): True
vertex orbits: 13  sizes: [1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]
orbit representatives: 003 004 013 014 023 024 031 032 034 113 122 123 222
full vertex list: 003 004 013 014 023 024 030 031 032 034 040 041 042 043 044 103 104 113 122 123 124 130 131 132 133 134 140 142 143 144 203 204 212 213 214 221 222 223 230 231 232 240 241 300 301 302 304 310 311 312 313 314 320 321 322 331 340 341 400 401 402 403 404 410 412 413 414 420 421 430 431 440 441
  003 (orbit 6) nbrs +x +y +z         spanned cell lacks vertex 114
  004 (orbit 6) nbrs +x +y -z         spanned cell lacks vertex 114
  013 (orbit 6) nbrs +x +y -y +z      opposite neighbours
  014 (orbit 6) nbrs +y -y -z         opposite neighbours
  023 (orbit 6) nbrs +x -y +z         spanned cell lacks vertex 114
  024 (orbit 6) nbrs +x +y -y -z      opposite neighbours
  031 (orbit 6) nbrs +x +y +z -z      opposite neighbours
  032 (orbit 6) nbrs +x +y -z         spanned cell lacks vertex 141
  034 (orbit 6) nbrs +x +y -y         opposite neighbours
  113 (orbit 6) nbrs +x -x +y -y      opposite neighbours
  122 (orbit 6) nbrs +x +y +z         spanned cell lacks vertex 233
  123 (orbit 6) nbrs +x -x +y -y +z -z opposite neighbours
  222 (orbit 1) nbrs +x -x +y -y +z -z opposite neighbours
x=0         x=1/2       x=1         x=3/2       x=2         x=5/2       x=3         x=7/2       x=4         
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