c_{ij} = a_ib_j \cap a_jb

c_ij = a_ib_j ∩a_jb_i

The picture above illustrates an example of a definition of a yellow line via

c_ij = a_ib_j ∩a_jb_i, i ≠ j.

Recall that the red lines are the a_i,…,a₆ and the blue lines are the b₁,…,b₆.

Recall that part of the conditions for a double six are that lines a_i and b_j intersect for all i ≠ j.

As two intersecting lines determine a plane, we have two planes a_ib_j and a_jb_i, indicated as colored triangles in the picture.

The two planes intersect in the line c_ij, indicated in yellow.

File translated from T_EX by T_TH, version 4.08.
On 4 Jun 2017, 11:23.