The output from the intersection_poset command concerns me. I typed the following
H5 = HyperplaneArrangements(QQ, ('x1', 'x2', 'x3', 'x4', 'x5'))
C5 = H5([(1, -2, 1, 0, 0), 0],[(1, -1, -1, 1, 0), 0], [(1, -1, 0, -1, 1), 0],[(0, 1, -2, 1, 0),0],[(0,1,-1,-1,1),0],[(0,0,1,-2,1),0],[(1,0,-2,0,1),0]);C5
p5 = C5.intersection_poset()
p5.plot()
where the last command prints out the (Hasse diagram of) intersection poset of C5. My direct calculation tells me that all of the rank-2 elements should be the joins of 3 atoms (rank-1 elements). Perhaps the discrepancy is due to linear dependence between the hyperplanes in C5. For instance, note that the second coefficient vector is the sum of the first and fourth.
I running SageMath 8.0. Perhaps this was fixed in some later version--I will seek an upgrade.
