map length (tiers :: [[ (Int,Int,Int) ]])  =  [1,3,6,10,15,21,...]

length (list :: [ (Int,Int,Int) ])  =  Infinity

allUnique (list :: [ (Int,Int,Int) ])  =  True

ratioRepetitions (list :: [ (Int,Int,Int) ])  =  0 % 1

tiers :: [(Int,Int,Int)]  =
  [ [(0,0,0)]
  , [ (0,0,1)
    , (0,1,0)
    , (1,0,0)
    ]
  , [ (0,0,-1)
    , (0,1,1)
    , (0,-1,0)
    , (1,0,1)
    , (1,1,0)
    , (-1,0,0)
    ]
  , [ (0,0,2)
    , (0,1,-1)
    , (0,-1,1)
    , (0,2,0)
    , (1,0,-1)
    , (1,1,1)
    , (1,-1,0)
    , (-1,0,1)
    , (-1,1,0)
    , (2,0,0)
    ]
  , [ (0,0,-2)
    , (0,1,2)
    , (0,-1,-1)
    , (0,2,1)
    , (0,-2,0)
    , (1,0,2)
    , (1,1,-1)
    , (1,-1,1)
    , (1,2,0)
    , (-1,0,-1)
    , (-1,1,1)
    , (-1,-1,0)
    , (2,0,1)
    , (2,1,0)
    , (-2,0,0)
    ]
  , [ (0,0,3)
    , (0,1,-2)
    , (0,-1,2)
    , (0,2,-1)
    , (0,-2,1)
    , (0,3,0)
    , (1,0,-2)
    , (1,1,2)
    , (1,-1,-1)
    , (1,2,1)
    , (1,-2,0)
    , (-1,0,2)
    , (-1,1,-1)
    , (-1,-1,1)
    , (-1,2,0)
    , (2,0,-1)
    , (2,1,1)
    , (2,-1,0)
    , (-2,0,1)
    , (-2,1,0)
    , (3,0,0)
    ]
  , ...
  ]