================================================================================
permrack4_1230
  exact dims  B_n (n=1..4): [4, 14, 47, 152]   K_n: [4, 14, 49, 171]   (B_n subset K_n verified)
  n=0: H_0 = 1 on both sides (del_1 = 0)
  n=1: H_n(B, del) = 1 ;  H_n(K, del) = H_n(M; Q) = 1   (exact over Q)
  n=2: H_n(B, del) = 0 ;  H_n(K, del) = H_n(M; Q) = 0   (exact over Q)
  n=3: H_n(B, del) = 1 ;  H_n(K, del) = H_n(M; Q) = 0   (exact over Q)
================================================================================
permrack3_120
  exact dims  B_n (n=1..4): [3, 7, 16, 33]   K_n: [3, 7, 16, 36]   (B_n subset K_n verified)
  n=0: H_0 = 1 on both sides (del_1 = 0)
  n=1: H_n(B, del) = 1 ;  H_n(K, del) = H_n(M; Q) = 1   (exact over Q)
  n=2: H_n(B, del) = 0 ;  H_n(K, del) = H_n(M; Q) = 0   (exact over Q)
  n=3: H_n(B, del) = 1 ;  H_n(K, del) = H_n(M; Q) = 0   (exact over Q)
