Every tetrachotomy is two dichotomies crossed. The four cells are the four small groups, four types each. Because any two Reinin dichotomies fix a third, each tetrachotomy also carries a hidden diagonal — shown on the cards tab — which is constant down each diagonal pair of cells.
After the 35-chart series compiled and drawn by Jared Vaughan. Group names and the Orbital/Content framing follow Kimani White; each card carries its own sources.
Any two of the fifteen land you on exactly one of the thirty-five. Pick the same one twice and you get the identity — no grouping at all. Pick two that are already in the same tetrachotomy and you get that same tetrachotomy back, from a different pair of handles.
Each column is one tetrachotomy; each cell names the small group that type belongs to.
Fifteen dichotomies, and any two of them fix a third: the product trait holds where the two agree and fails where they disagree. So dichotomies do not really come in pairs — they come in triads, {a, b, ab}, and a triad is what a tetrachotomy is. Two of the three are free; the third comes along whether you asked for it or not.
each triad contains 3 of those pairs
105 / 3 = 35 tetrachotomies
The same count from the other side: the fifteen plus the identity form a group of order sixteen, and a tetrachotomy is a four-element subgroup of it. There are exactly thirty-five. Nothing has been selected for interest — this is the whole list.
Write each dichotomy as the subset of {E, N, T, P} it depends on. Count how many of N and T appear. An even count — none or both — makes it Orbital: it is about the shape of the model, not about which elements fill it. An odd count makes it Content: it names which elements sit where.
The seven Orbital dichotomies are closed under the product, so they form a subgroup; the eight Content ones are the coset outside it. Two Contents always multiply to an Orbital, an Orbital and a Content always to a Content, two Orbitals always to an Orbital. Which fixes the shape of the whole list:
+ 28 Content pairs (each with 1 Orbital diagonal)
= 35 — and no triad is ever three Contents
Each of the seven Orbitals is the diagonal of exactly four Content pairs: 28 / 7 = 4. That is where the families of four come from — 8–11, 12–15, and so on to 32–35.
Primary (temperamental) Orbitals are Irrational–Rational, Extrovert–Introvert, Static–Dynamic; the other four are Secondary. Central to both Model A and Model G are Irrational–Rational, Process–Result and Democratic–Aristocratic — which is why 1–19 are shared by the two models and 20–35 are read off Model A alone.
Model A's eight positions carry three independent attributes — Strong (1,2,7,8), Inert (1,4,6,7), Valued (1,2,5,6). Multiply them the same way and four more appear, giving seven in all: Evaluative, Mental, Bold, Accepting. Eight positions, three generators — the small copy of the same machine that runs sixteen types on four.
Pick any two of those seven attributes and you pair the eight positions into four couples, ranked 4–3–2–1 twice over. That pairing is a level, and there are seven of them, one per triad — exactly as with the types.
Now the join. Each Content dichotomy is one position-attribute crossed with one aspect family:
So a tetrachotomy built from two Contents inherits their two attributes — and that pair is the level you read it at. Charts 20 and 21 pair Strong with Evaluative and so are read at Dimensionality; 22 and 23 pair Valued with Inert and are read at Priority. When both Contents carry the same attribute (16–19) the level collapses and the group is simply strong-versus-weak, inert-versus-contact, valued-versus-subdued, evaluative-versus-situational.
At T — Temperamental — Role equals Base. That is the one level where the first two positions do not separate, and it is why Temperaments (1) behaves unlike the rest.
All 35 tetrachotomies here, and all 140 of their small groups, were recomputed from the sign products and matched against the source charts cell by cell; the type lists agree everywhere. The 4–3–2–1 level readings on each card are generated from Model A, not transcribed. What is not settled by the algebra is what any of these groups means in behaviour: the names are the ones used by the authors credited on each card, and several of them disagree about content while agreeing exactly about membership.
For the same 35 drawn as full plates — coloured by level, with the diagonal shown on the corners and the Model A lines under every group — see Tetrachotomy Plates. The fifteen dichotomies underneath are in Reinin Drill.
Group names and the Orbital/Content framing follow Kimani White; individual tetrachotomies are credited on their cards to Ausra Augustinaviciute, Viktor Gulenko, Victor Talanov and Danidin, Grigory Mironov, Jack Oliver Aaron, Socion Archive, Sociotype.xyz, Varlawend, Jared Vaughan and u/Peppermint-Kiss. The 35-chart series these apps are built from was compiled and drawn by Jared Vaughan, who is also a named originator of 26 and 27.