The intersection lattice of a central hyperplane arrangement 
in a vector space 
consists of all intersections
of subcollections of 
, ordered by reverse inclusion.
The empty subcollection has intersection 
, which is the least element of
this partially ordered set (Anghel and Stan
2026).
The intersection lattice records which hyperplanes meet in each subspace. It is the combinatorial datum in Terao's conjecture. For a general affine hyperplane arrangement, the corresponding nonempty intersections form an intersection poset and need not form a lattice.
