We have computed to high accuracy the energies and the total widths of five triply excited n=2 intrashell resonances in He-, the 2s22p 2Po, 2s2p2 2De, 4Pe, 2Pe, and 2p3 2Do. These states are characterized by strong localized and asymptotic correlation effects and by their proximity to He doubly excited states. The possible many open channels correspond not only to one- but also to two-electron ... [Show full abstract] continua. The resonance parameters were established by applying the complex-coordinate rotation method with large basis sets of orbital and rij-correlated configurations. The expansion length of the trial wave functions went up to 1300 terms for the 2s2p2 2De resonance. This resonance is found to be below the He 2s2p 3Po threshold, in agreement with experimental observations and contrary to existing theoretical results. Similarly, the position of the 2s2p2 2Pe resonance is also below the He 2p2 3Pe threshold, in agreement with a recent theoretical prediction. The widths of these states range from 10 meV for the 2s2p2 4Pe to 331 meV for 2p3 2Do.