A review of some specific aspects of finite-size corner transfer matrices for free Fermion vertex systems in two-dimensional statistical mechanics is presented. Without being exhaustive, emphasis is being laid on the rôle of new special polynomials of the elliptic type which enclose a wide set of orthogonal polynomials known in the mathematical literature over the last seventy years. These polynomials help to verify neatly the predictions of conformal invariance for critical systems restricted to wedge shaped geometries and to prove some known facts about corner transfer matrices. Some extensions are presented and it is hoped that they might provide some hints for the understanding of connections between Virasoro symmetry, conformal invariance and quantum group symmetry occurring in the physics of exactly soluble models.