The term Enneagram triads is sometimes used to refer to the three Enneagram centers of intelligence. However, the centers only form one set of triads. There are four sets.
A set of triads is a grouping of the nine personality types into 3 groups of 3 for the purpose of exploring commonalities between the types within each group.
The triadic groupings are generally formed around types 3, 6, and 9 (the types indicated by the triangle of the Enneagram symbol).
The 1st set of triads are formed by looking one number to the right and one number to the left of types 3, 6, and 9.
This 1st set of triads is generally called the centers of intelligence or simply the centers. Most Enneagram authors and teachers teach the centers as a crucial part of the Enneagram types.
Starting with 3, 6, and 9 again, the 2nd triads are formed by looking two numbers to the right and two to the left.
The 2nd set of triads are not commonly used. One interpretation of the 2nd triads calls them Harmonic Groups where
The Harmonic Groups are a product of the Enneagram Institute and can be found in the book The Wisdom of the Enneagram.
When we look three to the right and three to the left of 3, 6, or 9 we simply end up with a triad consisting of 3, 6, and 9. Because of this the 3rd triads, unlike the 1st, 2nd, and 4th triads, don't center around 3, 6, and 9.
The 3rd set of triads aren't commonly used. There are two interpretations you may run across.
One interpretation of the 3rd triads originated from the Enneagram Institute called the Object Relations Groups where types
A second interpretation of the 3rd triads is called the Harmony Triads where types
The 4th triads again start with 3, 6, and 9 and look four to the right and four to the left.
The 4th set of triads are commonly used but not as much as the centers (1st triads). This set of triads is generally interpreted through Karen Horney's neurotic trends and associated types.