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Conjugate cone is a cone of the conjugate lattice defined as follows. That is, for subset A of standard lattice L3, Cone* A is a set of points (l, m, n) in R3  … Note that point (l, m, n) of the standard lattice  L3 corresponds to point ((-l+m+n)/2, (l-m+n)/2, (l+m-n)/2) of the conjugate lattice L3*. As shown below, Cone* A specifies “peaks and valleys” of the conjugate lattice … Since conjugate cones specify the “boundary” of slant triangles, we could call them “cotangent” cone.