Homonuclear spin-polarized alkali-metal trimers in their lowest-lying electronic state are investigated theoretically. Their equilibrium geometries and binding energies are determined with the state-of-the-art quantum chemical methods at three levels of approximation. The equilibrium geometries obtained Req(Li3)=3.100 \r{A}, Req(Na3)=4.353 \r{A}, Req(K3)=4.996 \r{A}, Req(Rb3)=5.391 \r{A}, and Req(Cs3)=5.730 \r{A} are compared to the other theoretical results and also with the very recent experimental results obtained through the laser-induced Coulomb explosion. Further theoretical studies are proposed, which could help with better interpretation of the experimental results for the sodium and cesium trimers.