The tritype assumes that we have a fixation in each center. One of them is the main fixation and corresponds to our core type.
The tritype was introduced independently by Ichazo and Katherine Fauvre around 1995 (according to her). The name was given by Katherine Fauvre, Ichazo did not give it a clear name. Ichazo’s interview (1996) describing the tritype for the first time is available here in Enneagram Monthly (beware that it is mixed with the subtypes by the journal in a very confusing way). He uses his own vocabulary.
Personally, I don’t know if the tritype is real or not.
The over-promotion of tritype is a bit of a problem. It may not be false as a theory, but it blurs the picture dangerously. The problem is not so much about the theory but about the way it is used.
After observing people for a long time, it turns out that arrows and wings are much more visible. The tritype should be accessed only long after the core type, wing and arrows have been stably observed. The tritype allows the misuse of the Enneagram as an identification to a type (as a sort of stereotype) to be pushed further, by mixing identifications. It becomes like inventing personalities and turns the Enneagram into an identification framework.
Focussing on wings and arrows prevents it because it shows, in a very practical way, how identification to a type can be an illusion. For example, the observation of a clear and unmistakable connection to type 1 (the easiest type to understand and feel viscerally) rules out all types not connected to 1 as a core type. This is especially useful to rule out type 6 that is much more difficult to understand than type 1.
The tritype is excessively promoted. It should remain a very advanced topic. Usually, the first move from using the Enneagram as an identification framework to seeing the fixations at play in our daily and ordinary life, requires to drop the tritype for a while. Each long-term mistyping is useful, a possible motivation, and allows to dive deeper into the knowledge of a type, while the tritype creates a falsely satisfying and shallow picture.
Enneagram Elements 