n = 4, k = 2 (a = n/2 - 1 = 1).  Expected: W_E, W_O ~ S^0; B^h ~ S^0 x S^0
   W_E = B minus O/G: H^i = {0: (2, [])}
   W_O = B minus E/G: H^i = {0: (2, [])}
   B^h = B minus (E/G u O/G): H^i = {0: (4, [])}
   E/G cells: H^i = E-type cells: 2, O-type cells: 2
n = 6, k = 3 (a = n/2 - 1 = 2).  Expected: W_E, W_O ~ S^1; B^h ~ S^1 x S^1
   W_E = B minus O/G: H^i = {1: (1, []), 0: (1, [])}
   W_O = B minus E/G: H^i = {1: (1, []), 0: (1, [])}
   B^h = B minus (E/G u O/G): H^i = {2: (1, []), 1: (2, []), 0: (1, [])}
   E/G cells: H^i = E-type cells: 12, O-type cells: 12
n = 8, k = 4 (a = n/2 - 1 = 3).  Expected: W_E, W_O ~ S^2; B^h ~ S^2 x S^2
   W_E = B minus O/G: H^i = {2: (1, []), 0: (1, [])}
   W_O = B minus E/G: H^i = {2: (1, []), 0: (1, [])}
   B^h = B minus (E/G u O/G): H^i = {4: (1, []), 2: (2, []), 0: (1, [])}
   E/G cells: H^i = E-type cells: 74, O-type cells: 74
