  The double and single differential cross-sections with respect to positron
and electron energies as well as the total cross-section of triplet production
in the laboratory frame are calculated numerically in order to develop a Monte
Carlo code for modelling electron-photon cascades in a soft photon field. To
avoid numerical integration irregularities of the integrands, which are
inherent to problems of this type, we have used suitable substitutions in
combination with a modern powerful program code Mathematica allowing one to
achieve reliable higher-precission results. The results obtained for the total
cross-section closely agree with others estimated analytically or by a
different numerical approach. The results for the double and single
differential cross-sections turn out to be somewhat different from some
reported recently. The mean energy of the produced particles, as a function of
the characteristic collisional parameter (the electron rest frame photon
energy), is calculated and approximated by an analytical expression that
revises other known approximations over a wide range of values of the argument.
The primary-electron energy loss rate due to triplet pair production is shown
to prevail over the inverse Compton scattering loss rate at several ($\sim$2)
orders of magnitude higher interaction energy than that predicted formerly.
