In the talk we will discuss approximative properties of the Taylor-Abel-Poisson linear summation method of Fourier series for functions of several variables that are periodic with respect to a hexagonal domain in the integral metric. In particular, direct and inverse theorems will be formulated in terms of approximations of functions by the Taylor-Abel-Poisson means and K-functionals generated by radial derivatives. Bernstein type inequalities will be given for L1-norm of radial derivatives of arbitrary order of the Poisson kernel.