intersection points of the 9 lines: 12 lines per point: {3}
triples with one vertex on each line: 4 partition of V: True
pencils normalised (G0 + Ginf proportional to the third singular member): OK
number of cubics: 8
BHRS p.7 Halphen cubics found among ours: 8 of 8
all 8 cubics smooth (partials generate all quartics): True
each cubic through exactly its 9 base vertices; at each vertex 6 cubics, 2 tangent lines, 3 cubics (3 pencils) per line: True
cross-pencil pairs (common vertices, shared tangents): [(6, 3)] count 24
no Halphen tangent equals a configuration line: True
t=8: monomials 45, conditions 60, exact rank 45, h^1(I_Z(t)) = 15, dim I_t = 0
t=9: monomials 55, conditions 60, exact rank 52, h^1(I_Z(t)) = 8, dim I_t = 3
t=10: monomials 66, conditions 60, exact rank 57, h^1(I_Z(t)) = 3, dim I_t = 9
t=11: monomials 78, conditions 60, exact rank 60, h^1(I_Z(t)) = 0, dim I_t = 18
t=12: monomials 91, conditions 60, exact rank 60, h^1(I_Z(t)) = 0, dim I_t = 31
