I used to have the old safari station 3433 years ago, & from what I can remember, the corner posts were a 4 way connector that had 2 of the base lattice supports going into them, & 2 of the triangle supports you are referring to on each corner of the building. They don't have an actual purpose as far as structural strength is concerned, but from what I can remember, the triangle supports in question seemed to fit snugly into the 4 way connector posts. I don't recall them falling out of place constantly, but it has been along time since I've had that set!