I just want to see if I can make the enneagram make as total sense as possible, in concise form.
So the organizing principle is first, you start with noting there are three triads. They are image/relations, adaptation/mind, and instinctual.
Their relation to each other is that instincts are the most basic sign of a need in the psyche to be fulfilled, which demonstrates that the ego is not inertial, but must act against entities apart from itself to survive. E9 represents the attempt to remain in the inertial state.
As instincts grow into more complicated emotions, two dominant movements of the emotional charge display themselves. One directs the emotions towards foreign bodies. The other directs emotions directly towards the ego-consciousness and its condition.
The most natural emotion towards foreign bodies covers their foreign-ness - hence this emotion is aversion. The most natural emotion towards the ego is a need for self-love. The instinctual natures differentiate into these emotions, and the precursors to doing so are the E8 and E1. With E1, there is not an open need for loving one's own image, hence in its instinctual form, the E1 reacts instinctually to an imperfect consciousness, with resentment, whenever it is not as it must be. Their sense of correctness often spills over to others as well, though this is more pronounced as greater consciousness of the outside is attained, which occurs as you move further rightward. With E8, there is an awareness of foreign bodies, but to maintain the instinctual state, and not allow the emotion of fear to arise, there is a forceful moving towards the foreign bodies that defies rhyme or reason, so that an intensity about this is almost conducted for its own sake. This is because moving towards is the opposite of aversion, which would entail moving away.
Much similarly, the E1, in resistance to the more open craving for self-love of the image triad, pursues perfection typically on the self's own principle, intensely moving away from the source of more complicated self-love emotions, often the result of weighing one's feelings about oneself against those of outside parties. The E8's force against the outside is mirrored by the E1's forcefulness towards himself/herself in correction.
The formation in full complexity of the aversion and self-love emotions accompanies greater and greater awareness of the differences between foreign bodies and the self. The image triad forms out of the latter, and it becomes fixated in the feeling center, because the more the more basic self-love emotion encounters foreigners (other people), the more this emotion complicates in relation to their perceptions of what worth entails. The intelligence center of feeling helps us relate to the worth of things, hence our associations with objective activities or our subjective consciousness is evaluated constantly through it, and as we know, the universality of a feeling judgment is determined on the theoretical ability for any human subject to participate in its realization. One could say the truth at work here is that all feelings in some sense occur relative to the feeling as to what one's own consciousness is like.
The fear triad forms out of the former, and the reason it resorts to the thinking/adaptive/mind activity is that the more foreign these foreign bodies are perceived as, the more it is impossible for the ego to deal directly with them, and it must thus abstract mind constructs from them as the only way of rendering them in a form acceptable to be dealt with by the self, that is, due to the mind constructs being a product of the self thus reducing the foreignness of the bodies one is averse to.
With every triad, the center type could be said to merge the ego with the pursuit of satiating the dominant emotion through the dominant intelligence center, hence why all of them link to E9 in a sense of "losing" their sense of ego to this pursuit. That is, the ego identifies so thoroughly with said center activity that insufficient friction is generated by the central activity to notice the ego's estrangedness from its pursuits, and hence to distinguish itself and know itself apart from them. The E6 may lose its identity apart from a system of reasonings (or at times something less theoretical) it follows. The E3 may identify thoroughly with the persona it has adopted in order to feel its own worth.
The other two types of a triad simply represent the tendency of the ego to be unable to accept the dominant "need." To illustrate, while the E6 hides behind a system of reasonings that it has reduced its existential experience of foreign bodies of, thus eliminating the ego's opposition to any given entity from the picture, the E5, closer to the triad of image, has a greater centeredness on the ego. While still identified with the mind center, it is more likely to see all systems of reasoning produced as arising from a definite sense of ego, and be more concerned with how in a sense they are identical with the sense of ego.
Some would try to call E5 the most mind-centered, but in my view none is more apt to let the mind completely take away their sense of identity than E6. I'd view the E5 in the sense of neighboring E4 as the most self/ego centered, in opposition to E9 which attempts to block a clear sense of ego, because when such a sense appears is when its estrangedness from the rest of the self becomes most apparent.
The self-centeredness may indeed view various mind constructs as basically equivalent to them, but the difference is the E6 attains awareness of itself through the systems generated, whereas for the E5 they are more an expression of its existence as removed from all else. It shows how a greater consciousness of a definite sense of ego increases as the sense of apartness from either objects of fear or objects which remind one of one's unfulfilled sense of self-love does.
I should add a note; being fixated corresponding to a center of intelligence does not imply that one functions mainly through that center. Only that one's motivations are understandable through it.