TII subcells for the Sp(8,R) x SO(7,2) block of Sp8
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cell#0 , |C| = 1
special orbit = [8]
special rep = [[4], []] , dim = 1
cell rep = phi[[4],[]]
TII depth = 1
TII multiplicity polynomial = X
TII subcells:
  tii[10,1] := {0}

cell#1 , |C| = 1
special orbit = [8]
special rep = [[4], []] , dim = 1
cell rep = phi[[4],[]]
TII depth = 1
TII multiplicity polynomial = X
TII subcells:
  tii[10,1] := {0}

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

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

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

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

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

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