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To specify affine closed trajectories, a particular type of conjugate cones, called conjugate roof, are used.

For subset A of standard lattice L3, Roof* A is a set of points (m+n. l+n. l+m) in R3 which satisfy …
Note that point m+n. l+n. l+m) of the standard lattice L3 corresponds to point (l, m, n) of the conjugate lattice L3*.

As shown below, Roof* A is obtained by putting as …
In this example, two cubes are put on Cone* A to obtain Roof* A which is equal to Cone* { x1l-1x2m-1x3n-1 }.