  In this work we derive a ready-to-use symmetry invariant expansion of the
full-zone 30-band k.p Hamiltonian for the Td point group. In order to find
respective parameters, the band structures of III-V materials were calculated
within a state-of-the-art Density Functional Theory (DFT) approach and used
next as targets to adjust the k.p bands. A satisfactory agreement of the k.p
model with the DFT band structures, for all the tested zinc blende III-V
semiconductors, has been achieved. Values of many of the parameters have not
been known so far. We also compare the fitted k.p parameters with the values
calculated using momentum matrix elements obtained directly from the DFT.
