W-representations carried by the wcells in SO(12,4) x SO(8,8) block of SO16

wcell#0:
  cardinality : 35
  special orbit : [9, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[], [5, 1, 1, 1]]
  cell representation : phi[[],[5, 1, 1, 1]]

wcell#1:
  cardinality : 250
  special orbit : [7, 3, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [4, 1, 1, 1]]
  cell representation : phi[[],[4, 2, 1, 1]]+phi[[1],[4, 1, 1, 1]]

wcell#2:
  cardinality : 336
  special orbit : [5, 5, 1, 1, 1, 1, 1, 1]
  special representation : [[2], [3, 1, 1, 1]]
  cell representation : phi[[],[3, 3, 1, 1]]+phi[[2],[3, 1, 1, 1]]

wcell#3:
  cardinality : 280
  special orbit : [5, 3, 3, 1, 1, 1, 1, 1]
  special representation : [[1], [3, 2, 1, 1]]
  cell representation : phi[[1],[3, 2, 1, 1]]

wcell#4:
  cardinality : 280
  special orbit : [5, 3, 3, 1, 1, 1, 1, 1]
  special representation : [[1], [3, 2, 1, 1]]
  cell representation : phi[[1],[3, 2, 1, 1]]

wcell#5:
  cardinality : 364
  special orbit : [3, 3, 3, 3, 1, 1, 1, 1]
  special representation : [[1, 1], [2, 2, 1, 1]]
  cell representation : phi[[1],[2, 2, 2, 1]]+phi[[1, 1],[2, 2, 1, 1]]

wcell#6:
  cardinality : 35
  special orbit : [7, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[], [4, 1, 1, 1, 1]]
  cell representation : phi[[],[4, 1, 1, 1, 1]]

wcell#7:
  cardinality : 35
  special orbit : [7, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[], [4, 1, 1, 1, 1]]
  cell representation : phi[[],[4, 1, 1, 1, 1]]

wcell#8:
  cardinality : 35
  special orbit : [7, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[], [4, 1, 1, 1, 1]]
  cell representation : phi[[],[4, 1, 1, 1, 1]]

wcell#9:
  cardinality : 184
  special orbit : [5, 3, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [3, 1, 1, 1, 1]]
  cell representation : phi[[],[3, 2, 1, 1, 1]]+phi[[1],[3, 1, 1, 1, 1]]

wcell#10:
  cardinality : 184
  special orbit : [5, 3, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [3, 1, 1, 1, 1]]
  cell representation : phi[[],[3, 2, 1, 1, 1]]+phi[[1],[3, 1, 1, 1, 1]]

wcell#11:
  cardinality : 140
  special orbit : [4, 4, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[2], [2, 1, 1, 1, 1]]
  cell representation : phi[[2],[2, 1, 1, 1, 1]]

wcell#12:
  cardinality : 21
  special orbit : [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[], [3, 1, 1, 1, 1, 1]]
  cell representation : phi[[],[3, 1, 1, 1, 1, 1]]

wcell#13:
  cardinality : 21
  special orbit : [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[], [3, 1, 1, 1, 1, 1]]
  cell representation : phi[[],[3, 1, 1, 1, 1, 1]]

wcell#14:
  cardinality : 68
  special orbit : [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [2, 1, 1, 1, 1, 1]]
  cell representation : phi[[],[2, 2, 1, 1, 1, 1]]+phi[[1],[2, 1, 1, 1, 1, 1]]

wcell#15:
  cardinality : 184
  special orbit : [5, 3, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [3, 1, 1, 1, 1]]
  cell representation : phi[[],[3, 2, 1, 1, 1]]+phi[[1],[3, 1, 1, 1, 1]]

wcell#16:
  cardinality : 184
  special orbit : [5, 3, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [3, 1, 1, 1, 1]]
  cell representation : phi[[],[3, 2, 1, 1, 1]]+phi[[1],[3, 1, 1, 1, 1]]

wcell#17:
  cardinality : 112
  special orbit : [3, 3, 3, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [2, 2, 1, 1, 1]]
  cell representation : phi[[1],[2, 2, 1, 1, 1]]

wcell#18:
  cardinality : 112
  special orbit : [3, 3, 3, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [2, 2, 1, 1, 1]]
  cell representation : phi[[1],[2, 2, 1, 1, 1]]

wcell#19:
  cardinality : 112
  special orbit : [3, 3, 3, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [2, 2, 1, 1, 1]]
  cell representation : phi[[1],[2, 2, 1, 1, 1]]

wcell#20:
  cardinality : 112
  special orbit : [3, 3, 3, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [2, 2, 1, 1, 1]]
  cell representation : phi[[1],[2, 2, 1, 1, 1]]

wcell#21:
  cardinality : 168
  special orbit : [3, 3, 2, 2, 1, 1, 1, 1, 1, 1]
  special representation : [[1, 1], [2, 1, 1, 1, 1]]
  cell representation : phi[[],[2, 2, 2, 1, 1]]+phi[[1, 1],[2, 1, 1, 1, 1]]

wcell#22:
  cardinality : 21
  special orbit : [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[], [3, 1, 1, 1, 1, 1]]
  cell representation : phi[[],[3, 1, 1, 1, 1, 1]]

wcell#23:
  cardinality : 21
  special orbit : [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[], [3, 1, 1, 1, 1, 1]]
  cell representation : phi[[],[3, 1, 1, 1, 1, 1]]

wcell#24:
  cardinality : 68
  special orbit : [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [2, 1, 1, 1, 1, 1]]
  cell representation : phi[[],[2, 2, 1, 1, 1, 1]]+phi[[1],[2, 1, 1, 1, 1, 1]]

wcell#25:
  cardinality : 68
  special orbit : [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [2, 1, 1, 1, 1, 1]]
  cell representation : phi[[],[2, 2, 1, 1, 1, 1]]+phi[[1],[2, 1, 1, 1, 1, 1]]

wcell#26:
  cardinality : 7
  special orbit : [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[], [2, 1, 1, 1, 1, 1, 1]]
  cell representation : phi[[],[2, 1, 1, 1, 1, 1, 1]]

wcell#27:
  cardinality : 7
  special orbit : [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[], [2, 1, 1, 1, 1, 1, 1]]
  cell representation : phi[[],[2, 1, 1, 1, 1, 1, 1]]

wcell#28:
  cardinality : 68
  special orbit : [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [2, 1, 1, 1, 1, 1]]
  cell representation : phi[[],[2, 2, 1, 1, 1, 1]]+phi[[1],[2, 1, 1, 1, 1, 1]]

wcell#29:
  cardinality : 68
  special orbit : [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [2, 1, 1, 1, 1, 1]]
  cell representation : phi[[],[2, 2, 1, 1, 1, 1]]+phi[[1],[2, 1, 1, 1, 1, 1]]

wcell#30:
  cardinality : 28
  special orbit : [2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1, 1], [1, 1, 1, 1, 1, 1]]
  cell representation : phi[[1, 1],[1, 1, 1, 1, 1, 1]]

wcell#31:
  cardinality : 7
  special orbit : [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[], [2, 1, 1, 1, 1, 1, 1]]
  cell representation : phi[[],[2, 1, 1, 1, 1, 1, 1]]

wcell#32:
  cardinality : 8
  special orbit : [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [1, 1, 1, 1, 1, 1, 1]]
  cell representation : phi[[1],[1, 1, 1, 1, 1, 1, 1]]

wcell#33:
  cardinality : 7
  special orbit : [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[], [2, 1, 1, 1, 1, 1, 1]]
  cell representation : phi[[],[2, 1, 1, 1, 1, 1, 1]]

wcell#34:
  cardinality : 8
  special orbit : [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [1, 1, 1, 1, 1, 1, 1]]
  cell representation : phi[[1],[1, 1, 1, 1, 1, 1, 1]]

wcell#35:
  cardinality : 1
  special orbit : [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[], [1, 1, 1, 1, 1, 1, 1, 1]]
  cell representation : phi[[],[1, 1, 1, 1, 1, 1, 1, 1]]

wcell#36:
  cardinality : 1
  special orbit : [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[], [1, 1, 1, 1, 1, 1, 1, 1]]
  cell representation : phi[[],[1, 1, 1, 1, 1, 1, 1, 1]]