This is the summary of lattices, cones, and roofs.
Firstly, standard cone Cone A is defined to …
As shown on the left, Cone A is used to …
Secondly, conjugate roof Roof* A is defined to …
As we will see later, Roof* A (or XRoof* A ) is used to …
Shown in the middle is the conjugate roof associated with Cone {p1, p2, p3} of the left figure.
And shown on the right is the extended conjugate roof associated with the cone.