The Shigesada-Kawasaki-Teramoto system, which consists of two
reaction-diffusion equations with variable cross-diffusion and quadratic
nonlinearities, is considered. The system is the most important case of the
biologically motivated model proposed by Shigesada et al. A complete
description of Lie symmetries for this system is derived. It is proved that the
Shigesada-Kawasaki-Teramoto system admits a wide range of different Lie
symmetries depending on coefficient values. In particular, the Lie symmetry
operators with highly unusual structure are unveiled and applied for finding
exact solutions of the relevant nonlinear system with cross-diffusion
