With the original use of the Enneagram symbol, the circle represented the clockwise movement of a process as it proceeded stepwise from point 1 to point 9. For the Enneagram personality types the circle is used in a different way.
The adjacent types or wings
It is sometimes said that a type is the product of the two types on either side as seen on the circle of the Enneagram symbol. Type 9 could then be thought of as a product of types 8 and 1.
Looking at this another way, the types on either side have a unique influence upon the type in the middle. This forms the basis of the wing theory in the Enneagram type system.
The opposite types
The concept of antipodes is briefly discussed by Claudio Naranjo in his book Character and Neurosis. He draws similarities between the types opposite one another on the circle (you have to disregard types 3, 6, and 9 to find these antipodes).
The three antipode pairs are: 1-5, 4-8, and 7-2.
Refer to Character and Neurosis for more.
Three groups of three
Triads group types around the circle to describe similarities between the three types in a group and differences between the groups themselves using concepts such as: centers of intelligence and stances.
Triads are discussed elsewhere on this website.
Type influences via the lines and arrows
The lines and arrows point to influences between the types around the circle such as: connecting points, stress/security points, and directions of integration/disintegration.
The lines and arrows are discussed elsewhere on this website.