Self-trapping on a generalized nonlinear tetrahedron

We analyze the dynamical self-trapping of an excitation propagating on a ge neralized n-sites tetrahedron, characterized by having every site at equal distance from each other. The evolution equation is given by the Discrete N onlinear Schrodinger (DNLS) equation. For completely localized initial cond itions, we find an exact solution for the critical nonlinearity strength (c hi/V)(c) as a function of the number of sites n of the generalized tetrahed ron. This critical nonlinearity, that marks the onset of the self-trapping transition, is always negative for n greater than or equal to 3 and its mag nitude increases monotonically with n, always remaining inside the sector d elimited by (\chi\/V) = n and (\X\/V) = 2n.