A measurement of the top quark pair production cross section in proton antiproton collisions at an interaction energy of $\sqrt{s}=1.96\text{ }\text{ }\mathrm{TeV}$ is presented. This analysis uses $405\ifmmode\pm\else\textpm\fi{}25\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$ of data collected with the D0 detector at the Fermilab Tevatron Collider. Fully hadronic $t\overline{t}$ decays with final states of six or more jets are separated from the multijet background using secondary vertex tagging and a neural network. The $t\overline{t}$ cross section is measured as ${\ensuremath{\sigma}}_{t\overline{t}}={4.5}_{\ensuremath{-}1.9}^{+2.0}(\mathrm{stat}{)}_{\ensuremath{-}1.1}^{+1.4}(\mathrm{syst})\ifmmode\pm\else\textpm\fi{}0.3(\mathrm{lumi})\text{ }\text{ }\mathrm{pb}$ for a top quark mass of ${m}_{t}=175\text{ }\text{ }\mathrm{GeV}/{c}^{2}$.