Next, let’s consider an equivalence relation on standard cones.
For subset A and B of standard lattice L3, …
Then, as shown below, In(A) is equal to In(B) if …
Shown on the left is the flow defined by Cone A, where A is given below.
Shown in the middle is the flow defined by another cone which is obtained by putting one cube (indicated by an arrow) on Cone A. By the construction, both cones are associated with the same standard roof. But their corresponding conjugate roofs, colored blue, are different from each other, as you see. Therefore, they are not equivalent and their closed trajectories sweep different areas on the hyperplane.
On the other hand, shown on the right is the flow defined by anther cone which is obtained by putting one more cube. By the construction, this cone is also associated with the same standard roof. Moreover, as you see, the right two cones share the same conjugate cone, colored blue. Therefore, they are equivalent and their closed trajectories sweep the same area on the hyperplane.