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If types are 16 and are caracterised by 15 orthogonal dichotomies, orthogonal quaternions would be exactly 140.
Some of them are well-known and named, (especially quadras, attitudes, temperaments, and rings of supervision), but some do not yet have an official name.
The socion is itself a Sedenion.
Octonionic masks (dichotomies) are 15, so the socion has 30 Octonions. (for example, the Sensory octonion has 8 types)
Quaternionic masks are 35, so the socion has 140 Quaternions. (for example, the Pragmatist (ST) quaternion has 4 types)