The head or thinking triad groups types five, six and seven. Like the other two, it belongs to a documented and recent lineage rather than to an inherited tradition, and stating that lineage accurately is the most useful thing a reference entry can do.
The nine-pointed figure was taught in the West by G. I. Gurdjieff in the first decades of the twentieth century as a diagram of process, without personality types. Oscar Ichazo mapped nine character types onto its points and taught them at his Arica school from the late nineteen sixties. Claudio Naranjo brought that material into psychotherapeutic settings in California in the early nineteen seventies, and the broad literature in circulation today, including the division into three centres of intelligence, descends from that period.
The head triad is the mental cluster, and the emotion the literature attaches to it is fear, presented in three modes: withdrawn and conserving at five, directly engaged with the question of safety at six, and outrun by anticipation and planning at seven. As with the other triads, the pattern of one emotion in three modes is a feature of the scheme rather than a finding about people.
Where the enneagram is used today it is used in coaching, in spiritual direction and in some clinical settings, and its empirical standing is contested. Anyone presenting it should say which lineage they are working in, since Ichazo and Naranjo and their respective successors do not agree on all of it, and the disagreements reach the triads.
Sources The Enneagram: G. I. Gurdjieff's Esoteric SymbolCarole M. Cusack with The Enneagram: A systematic review of the literature and directions for future researchJoshua N. Hook, Todd W. Hall, Don E. Davis, Daryl R. Van Tongeren and Mackenzie Conner