The number of edges eminating from a vertex v is called
   the "degree" (or "valence") of v.

   Group              Elements      Diameter     Valence (or # of generators)
   -----              --------      --------     -------

  slice-squared           8            3            3
  <U2, R2>               12            6            2
  <U2, D2, F2>           96           10            3
  <U2, D2, F2, B2>      192            8            4
  <U2, F2, R2>        2,592           14            3
  squares group     663,552           15            6
  <U,D,L,R,F,B>   4.3x10^19           ??           12

  Long-form number of elements of puzzles
  ---------------------------------------


  Rubik's Wahn (5x5x5) 282,870,942,277,741,856,536,180,333,107,150,328,293,127,731,985,672,134,721,536,000,000,000,000,000
  Megaminx             100,669,616,553,523,347,122,516,032,313,645,505,168,688,116,411,019,768,627,200,000,000,000
  Rubik's Revenge (4x4x4)    7,401,196,841,564,901,869,874,093,974,498,574,336,000,000,000
  Alexander's Star          72,431,714,252,715,638,411,621,302,272,000,000
  VIP Sphere                           437,763,136,697,395,052,544,000,000
  Rubik's Cube (3x3x3)                          43,252,003,274,489,856,000
  <U2,D2,L,R,F,B> subgroup			    21,119,142,223,872,000
  Square 1                                              11,958,666,854,400
  <U2,D2,L2,R2,F,B> subgroup                                19,508,428,800
  Rubik's Domino (3x3x2)                                       406,425,600
  Rainbow Cube                                                 239,500,800 
  Pyraminx                                                      75,582,720
  Dino Cube                                                     19,958,400
  Halpern-Meier Tetrahedron                                      3,732,480