Wall

A wall is an unordered pair of complementary halfspaces $\{W^{+},W^{-}\}$.

A halfspace is one of the two complementary parts determined by a wall.

Two walls cross when all four intersections of one halfspace from each wall are nonempty. A collection of pairwise crossing walls is also called transverse.

A transverse collection of walls is a collection in which every two distinct walls cross.