Are the inner lines of the Enneagram symbol useful as applied to the types?

[Dave]

The inner lines of the Enneagram symbol are used to show the relationship between steps in a process when used in the Gurdjieff tradition (The Enneagram as Process). The Enneatypes don't use the Enneagram to understand a process, instead it presents the relationships between nine distinct entities or types.

Are the inner lines valid for use with the personality types?

I've stated my observations in two blog articles:
Contradictions Between the Triads and the Inner Lines
Alternative to the Inner Lines and Tritypes - Tricenters

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