The only possible starter triangles (i.e. three types that are weak to one another in a rock-paper-scissors fashion and the same with resistances in reverse) other than the traditional Fire/Water/Grass are Rock/Fighting/Flying, Fire/Rock/Steel and Grass/Poison/Ground. No, Dark/Psychic/Fighting does not qualify. The reason they don't is that while Dark is super effective on Psychic which is super effective on Fighting which is super effective on Dark, it doesn't go the other way. With Fire, Water and Grass, Grass is not very effective on Fire which is not very effective on Water which is not very effective on Grass. With Dark, Psychic and Fighting, Dark is not very effective on Fighting which is not very effective on Psychic which is INNEFECTIVE on Dark. There's an imbalance on one side of the triangle compared to the others, and that breaks it. By the same logic, Water/Ground/Electric is also unbalanced, and in fact even more so: Ground deals neutral damage to Water, which deals neutral damage to Electric, which deals NO damage to Ground. The Electric-type facing off against the Ground-type is much worse off than the Ground-type would be facing off against the Water-type. It's just not fair, and the whole point of the starter triangle is that no starter is better off typewise against the rival's starter than any other. We are not likely to get different starter triangles, anyway; Fire, Water and Grass are both traditional and make sense as representatives of three elements while the other triangles are pretty much out-of-the-blue incidental relations that happen to emerge from the type chart.
