What we consider next is cell complexes on R 2 with a Z 2 lattice group (p = 0). Dashed line shows a lattice cell, and for brevity, we always suppose K l = K 3 , if l ≥ 4 : However, β l,0 k (K) = 0 for countable cell-complex K and its filtration, which verifies result in Corollary 5.