  For classical groups SL(n), SO(n) and Sp(2n), we define uniformly geometric
valuations on the corresponding complete flag varieties. The valuation in every
type comes from a natural coordinate system on the open Schubert cell and is
combinatorially related to the Gelfand-Zetlin pattern in the same type. In
types A and C, we identify the corresponding Newton-Okounkov polytopes with the
Feigin-Fourier-Littelmann-Vinberg polytopes. In types B and D, we compute
low-dimensional examples and formulate open questions.
