TII subcells for the SO(7,6) x Sp(5,1) block of SO13
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cell#0 , |C| = 1
special orbit = [13]
special rep = [[6], []] , dim = 1
cell rep = phi[[6],[]]
TII depth = 1
TII multiplicity polynomial = X
TII subcells:
  tii[26,1] := {0}

cell#1 , |C| = 11
special orbit = [11, 1, 1]
special rep = [[5], [1]] , dim = 6
cell rep = phi[[5, 1],[]]+phi[[5],[1]]
TII depth = 1
TII multiplicity polynomial = 5*X^2+X
TII subcells:
  tii[25,1] := {2, 10}
  tii[25,2] := {0, 9}
  tii[25,3] := {1, 8}
  tii[25,4] := {3, 7}
  tii[25,5] := {4, 6}
  tii[25,6] := {5}

cell#2 , |C| = 24
special orbit = [9, 2, 2]
special rep = [[4, 1], [1]] , dim = 24
cell rep = phi[[4, 1],[1]]
TII depth = 4
TII multiplicity polynomial = 24*X
TII subcells:
  tii[23,1] := {2}
  tii[23,2] := {6}
  tii[23,3] := {11}
  tii[23,4] := {21}
  tii[23,5] := {23}
  tii[23,6] := {0}
  tii[23,7] := {18}
  tii[23,8] := {1}
  tii[23,9] := {14}
  tii[23,10] := {3}
  tii[23,11] := {10}
  tii[23,12] := {7}
  tii[23,13] := {22}
  tii[23,14] := {17}
  tii[23,15] := {4}
  tii[23,16] := {13}
  tii[23,17] := {5}
  tii[23,18] := {9}
  tii[23,19] := {20}
  tii[23,20] := {16}
  tii[23,21] := {8}
  tii[23,22] := {12}
  tii[23,23] := {19}
  tii[23,24] := {15}