Sociotypes as Isomorphisms Between Dichotomy Systems (and Automorphisms on Partitions of a Set)

If you want to see which dichotomy systems I'm using for Model G, check out this post (https://varlawend.blogspot.com/2023/06/mathematical-discovery-model-g-has-its.html). They are either new or eclectic, so you might not recognize them.

If you want to see the proof that these mappings are all isomorphisms (i.e. they are obviously one-to-one bijective mappings, but it has to be proved that they preserve the structure of the dichotomy systems and interleaving operation), check out this post (https://varlawend.blogspot.com/2023/06/encyclopedia-of-model-g-and-model.html), particularly the sections about Types as Isomorphisms and more General Model A and G Proofs, Set of Bijective Mappings Between Model A Elemental and Functional/Positional Blocking Sets, Set of Bijective Mappings Between Model G Elemental and Functional/Positional Blocking Sets, and Proof of Sociotypes as Isomorphisms.

First, we are first going to map the Gulenko-Newman elemental dichotomies to the Gulenko-Newman functional/positional dichotomies 16 times, which shows the types as isomorphisms of Model G dichotomy systems. However, it is possible to do the mapping in the reverse direction (f/p dichotomies to e dichotomies), and it is possible to create such mappings using Model A dichotomy systems, which we will do in the next section.

Since these isomorphisms are themselves isomorphic to an automorphism, the Sociotypes can also be considered automorphisms from the set of all 35 dichotomous partitions of the numbers 1 through 8 to itself (up to a different naming scheme for the 8 elements of Socionics), in such a way as to combine both Model A and Model G dichotomy systems. We will show that in the final section.

Types as Isomorphisms in Model G Dichotomy Systems

ILE Isomorphism from elements to positions:
Static <-> Opening
Dynamic <-> Closing
Irrational <-> Stable
Rational <-> Unstable
Extroverted <-> Externality
Introverted <-> Internality
LII+EIE HEF <-> Excitable
ESI+LSE HEF <-> Inhibitable
LIE+EII HEF <-> Tensioned
ESE+LSI HEF <-> Relaxed
ILE+SLI HEF <-> Energetic
SEE+IEI HEF <-> Informational
IEE+SEI HEF <-> Impressionable
SLE+ILI HEF <-> Unimpressionable

SEI Isomorphism from elements to positions:
Static <-> Closing
Dynamic <-> Opening
Irrational <-> Stable
Rational <-> Unstable
Extroverted <-> Internality
Introverted <-> Externality
LII+EIE HEF <-> Relaxed
ESI+LSE HEF <-> Tensioned
LIE+EII HEF <-> Inhibitable
ESE+LSI HEF <-> Excitable
ILE+SLI HEF <-> Impressionable
SEE+IEI HEF <-> Unimpressionable
IEE+SEI HEF <-> Energetic
SLE+ILI HEF <-> Informational

ESE Isomorphism from elements to positions:
Static <-> Closing
Dynamic <-> Opening
Irrational <-> Unstable
Rational <-> Stable
Extroverted <-> Externality
Introverted <-> Internality
LII+EIE HEF <-> Impressionable
ESI+LSE HEF <-> Unimpressionable
LIE+EII HEF <-> Informational
ESE+LSI HEF <-> Energetic
ILE+SLI HEF <-> Relaxed
SEE+IEI HEF <-> Tensioned
IEE+SEI HEF <-> Excitable
SLE+ILI HEF <-> Inhibitable

LII Isomorphism from elements to positions:

Static <-> Opening
Dynamic <-> Closing
Irrational <-> Unstable
Rational <-> Stable
Extroverted <-> Internality
Introverted <-> Externality
LII+EIE HEF <-> Energetic
ESI+LSE HEF <-> Informational
LIE+EII HEF <-> Unimpressionable
ESE+LSI HEF <-> Impressionable
ILE+SLI HEF <-> Excitable
SEE+IEI HEF <-> Inhibitable
IEE+SEI HEF <-> Relaxed
SLE+ILI HEF <-> Tensioned

EIE Isomorphism from elements to positions:

Static <-> Closing
Dynamic <-> Opening
Irrational <-> Unstable
Rational <-> Stable
Extroverted <-> Externality
Introverted <-> Internality
LII+EIE HEF <-> Energetic
ESI+LSE HEF <-> Informational
LIE+EII HEF <-> Unimpressionable
ESE+LSI HEF <-> Impressionable
ILE+SLI HEF <-> Inhibitable
SEE+IEI HEF <-> Excitable
IEE+SEI HEF <-> Tensioned

SLE+ILI HEF <-> Relaxed

LSI Isomorphism from elements to positions:

Static <-> Opening
Dynamic <-> Closing
Irrational <-> Unstable
Rational <-> Stable
Extroverted <-> Internality
Introverted <-> Externality
LII+EIE HEF <-> Impressionable
ESI+LSE HEF <-> Unimpressionable
LIE+EII HEF <-> Informational
ESE+LSI HEF <-> Energetic
ILE+SLI HEF <-> Tensioned
SEE+IEI HEF <-> Relaxed
IEE+SEI HEF <-> Inhibitable
SLE+ILI HEF <-> Excitable

SLE Isomorphism from elements to positions:

Static <-> Opening
Dynamic <-> Closing
Irrational <-> Stable
Rational <-> Unstable
Extroverted <-> Externality
Introverted <-> Internality
LII+EIE HEF <-> Relaxed
ESI+LSE HEF <-> Tensioned
LIE+EII HEF <-> Inhibitable
ESE+LSI HEF <-> Excitable

ILE+SLI HEF <-> Unimpressionable
SEE+IEI HEF <-> Impressionable
IEE+SEI HEF <-> Informational
SLE+ILI HEF <-> Energetic

IEI Isomorphism from elements to positions:

Static <-> Closing
Dynamic <-> Opening
Irrational <-> Stable
Rational <-> Unstable
Extroverted <-> Internality
Introverted <-> Externality
LII+EIE HEF <-> Excitable
ESI+LSE HEF <-> Inhibitable
LIE+EII HEF <-> Tensioned
ESE+LSI HEF <-> Relaxed
ILE+SLI HEF <-> Informational
SEE+IEI HEF <-> Energetic
IEE+SEI HEF <-> Unimpressionable
SLE+ILI HEF <-> Impressionable

SEE Isomorphism from elements to positions:

Static <-> Opening
Dynamic <-> Closing
Irrational <-> Stable
Rational <-> Unstable
Extroverted <-> Externality
Introverted <-> Internality
LII+EIE HEF <-> Inhibitable
ESI+LSE HEF <-> Excitable
LIE+EII HEF <-> Relaxed
ESE+LSI HEF <-> Tensioned

ILE+SLI HEF <-> Informational
SEE+IEI HEF <-> Energetic
IEE+SEI HEF <-> Unimpressionable
SLE+ILI HEF <-> Impressionable

ILI Isomorphism from elements to positions:

Static <-> Closing
Dynamic <-> Opening
Irrational <-> Stable
Rational <-> Unstable
Extroverted <-> Internality
Introverted <-> Externality
LII+EIE HEF <-> Tensioned
ESI+LSE HEF <-> Relaxed
LIE+EII HEF <-> Excitable
ESE+LSI HEF <-> Inhibitable
ILE+SLI HEF <-> Unimpressionable
SEE+IEI HEF <-> Impressionable
IEE+SEI HEF <-> Informational
SLE+ILI HEF <-> Energetic

LIE Isomorphism from elements to positions:

Static <-> Closing
Dynamic <-> Opening
Irrational <-> Unstable
Rational <-> Stable
Extroverted <-> Externality
Introverted <-> Internality
LII+EIE HEF <-> Unimpressionable
ESI+LSE HEF <-> Impressionable
LIE+EII HEF <-> Energetic
ESE+LSI HEF <-> Informational
ILE+SLI HEF <-> Tensioned
SEE+IEI HEF <-> Relaxed
IEE+SEI HEF <-> Inhibitable

SLE+ILI HEF <-> Excitable

ESI Isomorphism from elements to positions:

Static <-> Opening
Dynamic <-> Closing
Irrational <-> Unstable
Rational <-> Stable
Extroverted <-> Internality
Introverted <-> Externality
LII+EIE HEF <-> Informational
ESI+LSE HEF <-> Energetic
LIE+EII HEF <-> Impressionable
ESE+LSI HEF <-> Unimpressionable
ILE+SLI HEF <-> Inhibitable
SEE+IEI HEF <-> Excitable
IEE+SEI HEF <-> Tensioned
SLE+ILI HEF <-> Relaxed

LSE Isomorphism from elements to positions:

Static <-> Closing
Dynamic <-> Opening
Irrational <-> Unstable
Rational <-> Stable
Extroverted <-> Externality
Introverted <-> Internality
LII+EIE HEF <-> Informational
ESI+LSE HEF <-> Energetic
LIE+EII HEF <-> Impressionable
ESE+LSI HEF <-> Unimpressionable
ILE+SLI HEF <-> Excitable
SEE+IEI HEF <-> Inhibitable
IEE+SEI HEF <-> Relaxed

SLE+ILI HEF <-> Tensioned

EII Isomorphism from elements to positions:

Static <-> Opening
Dynamic <-> Closing
Irrational <-> Unstable
Rational <-> Stable
Extroverted <-> Internality
Introverted <-> Externality
LII+EIE HEF <-> Unimpressionable
ESI+LSE HEF <-> Impressionable
LIE+EII HEF <-> Energetic
ESE+LSI HEF <-> Informational
ILE+SLI HEF <-> Relaxed
SEE+IEI HEF <-> Tensioned
IEE+SEI HEF <-> Excitable
SLE+ILI HEF <-> Inhibitable

IEE Isomorphism from elements to positions:

Static <-> Opening
Dynamic <-> Closing
Irrational <-> Stable
Rational <-> Unstable
Extroverted <-> Externality
Introverted <-> Internality
LII+EIE HEF <-> Tensioned
ESI+LSE HEF <-> Relaxed
LIE+EII HEF <-> Excitable
ESE+LSI HEF <-> Inhibitable

ILE+SLI HEF <-> Impressionable
SEE+IEI HEF <-> Unimpressionable
IEE+SEI HEF <-> Energetic
SLE+ILI HEF <-> Informational

SLI Isomorphism from elements to positions:

Static <-> Closing
Dynamic <-> Opening
Irrational <-> Stable
Rational <-> Unstable
Extroverted <-> Internality
Introverted <-> Externality
LII+EIE HEF <-> Inhibitable
ESI+LSE HEF <-> Excitable
LIE+EII HEF <-> Relaxed
ESE+LSI HEF <-> Tensioned
ILE+SLI HEF <-> Energetic
SEE+IEI HEF <-> Informational
IEE+SEI HEF <-> Impressionable
SLE+ILI HEF <-> Unimpressionable

There are a lot of interesting similarities here, including between the types that share the same activity orientation shift group (https://socioniks.net/article/?id=152).

____________

Types as Isomorphisms in Model A Dichotomy Systems

The elemental system of dichotomies I'm using can be found here (https://www.wikisocion.net/en/index.php/Information_elements#Information_Element_Dichotomies).

The functional/positional system of dichotomies I'm using can be found here (https://www.wikisocion.net/en/index.php/Function_dichotomies).

ILE Isomorphism from elements to positions:
Static <-> Mental
Dynamic <-> Vital
Irrational <-> Accepting
Rational <-> Producing
Extroverted <-> Bold
Introverted <-> Cautious
Detached <-> Strong
Involved <-> Weak
Implicit <-> Inert
Explicit <-> Contact
Alpha <-> Valued
Gamma <-> Unvalued
Delta <-> Evaluative
Beta <-> Situational

SEI Isomorphism from elements to positions:
Static <-> Vital
Dynamic <-> Mental
Irrational <-> Accepting
Rational <-> Producing
Extroverted <-> Cautious
Introverted <-> Bold
Detached <-> Weak
Involved <-> Strong
Implicit <-> Contact
Explicit <-> Inert
Alpha <-> Valued
Gamma <-> Unvalued
Delta <-> Evaluative
Beta <-> Situational

ESE Isomorphism from elements to positions:
Static <-> Vital
Dynamic <-> Mental
Irrational <-> Producing
Rational <-> Accepting
Extroverted <-> Bold
Introverted <-> Cautious
Detached <-> Weak
Involved <-> Strong
Implicit <-> Inert
Explicit <-> Contact
Alpha <-> Valued
Gamma <-> Unvalued
Delta <-> Situational
Beta <-> Evaluative

LII Isomorphism from elements to positions:

Static <-> Mental
Dynamic <-> Vital
Irrational <-> Producing
Rational <-> Accepting
Extroverted <-> Cautious
Introverted <-> Bold
Detached <-> Strong
Involved <-> Weak
Implicit <-> Contact
Explicit <-> Inert
Alpha <-> Valued
Gamma <-> Unvalued
Delta <-> Situational
Beta <-> Evaluative

EIE Isomorphism from elements to positions:

Static <-> Vital
Dynamic <-> Mental
Irrational <-> Producing
Rational <-> Accepting
Extroverted <-> Bold
Introverted <-> Cautious
Detached <-> Contact
Involved <-> Inert
Implicit <-> Strong
Explicit <-> Weak
Alpha <-> Evaluative
Gamma <-> Situational
Delta <-> Unvalued
Beta <-> Valued

LSI Isomorphism from elements to positions:

Static <-> Mental
Dynamic <-> Vital
Irrational <-> Producing
Rational <-> Accepting
Extroverted <-> Cautious
Introverted <-> Bold
Detached <-> Inert
Involved <-> Contact
Implicit <-> Weak
Explicit <-> Strong
Alpha <-> Evaluative
Gamma <-> Situational
Delta <-> Unvalued
Beta <-> Valued

SLE Isomorphism from elements to positions:

Static <-> Mental
Dynamic <-> Vital
Irrational <-> Accepting
Rational <-> Producing
Extroverted <-> Bold
Introverted <-> Cautious
Detached <-> Contact
Involved <-> Inert
Implicit <-> Weak
Explicit <-> Strong
Alpha <-> Situational
Gamma <-> Evaluative
Delta <-> Unvalued
Beta <-> Valued

IEI Isomorphism from elements to positions:

Static <-> Vital
Dynamic <-> Mental
Irrational <-> Accepting
Rational <-> Producing
Extroverted <-> Cautious
Introverted <-> Bold
Detached <-> Inert
Involved <-> Contact
Implicit <-> Strong
Explicit <-> Weak
Alpha <-> Situational
Gamma <-> Evaluative
Delta <-> Unvalued
Beta <-> Valued

SEE Isomorphism from elements to positions:

Static <-> Mental
Dynamic <-> Vital
Irrational <-> Accepting
Rational <-> Producing
Extroverted <-> Bold
Introverted <-> Cautious
Detached <-> Weak
Involved <-> Strong
Implicit <-> Contact
Explicit <-> Inert
Alpha <-> Unvalued
Gamma <-> Valued
Delta <-> Situational
Beta <-> Evaluative

ILI Isomorphism from elements to positions:

Static <-> Vital
Dynamic <-> Mental
Irrational <-> Accepting
Rational <-> Producing
Extroverted <-> Cautious
Introverted <-> Bold
Detached <-> Strong
Involved <-> Weak
Implicit <-> Inert
Explicit <-> Contact
Alpha <-> Unvalued
Gamma <-> Valued
Delta <-> Situational
Beta <-> Evaluative

LIE Isomorphism from elements to positions:

Static <-> Vital
Dynamic <-> Mental
Irrational <-> Producing
Rational <-> Accepting
Extroverted <-> Bold
Introverted <-> Cautious
Detached <-> Strong
Involved <-> Weak
Implicit <-> Contact
Explicit <-> Inert
Alpha <-> Unvalued
Gamma <-> Valued
Delta <-> Evaluative
Beta <-> Situational

ESI Isomorphism from elements to positions:

Static <-> Mental
Dynamic <-> Vital
Irrational <-> Producing
Rational <-> Accepting
Extroverted <-> Cautious
Introverted <-> Bold
Detached <-> Weak
Involved <-> Strong
Implicit <-> Inert
Explicit <-> Contact
Alpha <-> Unvalued
Gamma <-> Valued
Delta <-> Evaluative
Beta <-> Situational

LSE Isomorphism from elements to positions:

Static <-> Vital
Dynamic <-> Mental
Irrational <-> Producing
Rational <-> Accepting
Extroverted <-> Bold
Introverted <-> Cautious
Detached <-> Inert
Involved <-> Contact
Implicit <-> Weak
Explicit <-> Strong
Alpha <-> Situational
Gamma <-> Evaluative
Delta <-> Valued
Beta <-> Unvalued

EII Isomorphism from elements to positions:

Static <-> Mental
Dynamic <-> Vital
Irrational <-> Producing
Rational <-> Accepting
Extroverted <-> Cautious
Introverted <-> Bold
Detached <-> Contact
Involved <-> Inert
Implicit <-> Strong
Explicit <-> Weak
Alpha <-> Situational
Gamma <-> Evaluative
Delta <-> Valued
Beta <-> Unvalued

IEE Isomorphism from elements to positions:

Static <-> Mental
Dynamic <-> Vital
Irrational <-> Accepting
Rational <-> Producing
Extroverted <-> Bold
Introverted <-> Cautious
Detached <-> Inert
Involved <-> Contact
Implicit <-> Strong
Explicit <-> Weak
Alpha <-> Evaluative
Gamma <-> Situational
Delta <-> Valued
Beta <-> Unvalued

SLI Isomorphism from elements to positions:

Static <-> Vital
Dynamic <-> Mental
Irrational <-> Accepting
Rational <-> Producing
Extroverted <-> Cautious
Introverted <-> Bold
Detached <-> Contact
Involved <-> Inert
Implicit <-> Weak
Explicit <-> Strong
Alpha <-> Evaluative
Gamma <-> Sitiuational
Delta <-> Valued
Beta <-> Unvalued

As you can see, there are also a lot of interesting structural patterns here!

____________

Now let's show the entire set of 16 "automorphisms" (at least, all partitions under them which produce valid dichotomies for a Socionics dichotomy system, since all the invalid partitions are also mapped albeit to mutually irrelevant partitions with no significant structural restraints imposed on them, so their mappings are trivial). They combine models A and G together to describe the types with unprecedented mathematical completeness:

ILE Automorphism from elements to positions:
Static <-> Opening (Mental)
Dynamic <-> Closing (Vital)
Irrational <-> Stable (Accepting)
Rational <-> Unstable (Producing)
Extroverted <-> Externality (Bold)
Introverted <-> Internality (Cautious)
LII+EIE HEF <-> Excitable
ESI+LSE HEF <-> Inhibitable
LIE+EII HEF <-> Tensioned
ESE+LSI HEF <-> Relaxed
ILE+SLI HEF <-> Energetic
SEE+IEI HEF <-> Informational
IEE+SEI HEF <-> Impressionable
SLE+ILI HEF <-> Unimpressionable

Detached <-> Strong
Involved <-> Weak
Implicit <-> Inert
Explicit <-> Contact
Alpha <-> Valued
Gamma <-> Unvalued
Delta <-> Evaluative
Beta <-> Situational

SEI Automorphism from elements to positions:
Static <-> Closing (Vital)
Dynamic <-> Opening (Mental)
Irrational <-> Stable (Accepting)
Rational <-> Unstable (Producing)
Extroverted <-> Internality (Cautious)
Introverted <-> Externality (Bold)
LII+EIE HEF <-> Relaxed
ESI+LSE HEF <-> Tensioned
LIE+EII HEF <-> Inhibitable
ESE+LSI HEF <-> Excitable
ILE+SLI HEF <-> Impressionable
SEE+IEI HEF <-> Unimpressionable
IEE+SEI HEF <-> Energetic
SLE+ILI HEF <-> Informational

Detached <-> Weak
Involved <-> Strong
Implicit <-> Contact
Explicit <-> Inert
Alpha <-> Valued
Gamma <-> Unvalued
Delta <-> Evaluative
Beta <-> Situational

ESE Automorphism from elements to positions:
Static <-> Closing (Vital)
Dynamic <-> Opening (Mental)
Irrational <-> Unstable (Producing)
Rational <-> Stable (Accepting)
Extroverted <-> Externality (Bold)
Introverted <-> Internality (Cautious)
LII+EIE HEF <-> Impressionable
ESI+LSE HEF <-> Unimpressionable
LIE+EII HEF <-> Informational
ESE+LSI HEF <-> Energetic
ILE+SLI HEF <-> Relaxed
SEE+IEI HEF <-> Tensioned
IEE+SEI HEF <-> Excitable
SLE+ILI HEF <-> Inhibitable

Detached <-> Weak
Involved <-> Strong
Implicit <-> Inert
Explicit <-> Contact
Alpha <-> Valued
Gamma <-> Unvalued
Delta <-> Situational
Beta <-> Evaluative

LII Automorphism from elements to positions:

Static <-> Opening (Mental)
Dynamic <-> Closing (Vital)
Irrational <-> Unstable (Producing)
Rational <-> Stable (Accepting)
Extroverted <-> Internality (Cautious)
Introverted <-> Externality (Bold)
LII+EIE HEF <-> Energetic
ESI+LSE HEF <-> Informational
LIE+EII HEF <-> Unimpressionable
ESE+LSI HEF <-> Impressionable
ILE+SLI HEF <-> Excitable
SEE+IEI HEF <-> Inhibitable
IEE+SEI HEF <-> Relaxed
SLE+ILI HEF <-> Tensioned

Detached <-> Strong
Involved <-> Weak
Implicit <-> Contact
Explicit <-> Inert
Alpha <-> Valued
Gamma <-> Unvalued
Delta <-> Situational
Beta <-> Evaluative

EIE Automorphism from elements to positions:

Static <-> Closing (Vital)
Dynamic <-> Opening (Mental)
Irrational <-> Unstable (Producing)
Rational <-> Stable (Accepting)
Extroverted <-> Externality (Bold)
Introverted <-> Internality (Cautious)
LII+EIE HEF <-> Energetic
ESI+LSE HEF <-> Informational
LIE+EII HEF <-> Unimpressionable
ESE+LSI HEF <-> Impressionable
ILE+SLI HEF <-> Inhibitable
SEE+IEI HEF <-> Excitable
IEE+SEI HEF <-> Tensioned

SLE+ILI HEF <-> Relaxed

Detached <-> Contact
Involved <-> Inert
Implicit <-> Strong
Explicit <-> Weak
Alpha <-> Evaluative
Gamma <-> Situational
Delta <-> Unvalued
Beta <-> Valued

LSI Automorphism from elements to positions:

Static <-> Opening (Mental)
Dynamic <-> Closing (Vital)
Irrational <-> Unstable (Producing)
Rational <-> Stable (Accepting)
Extroverted <-> Internality (Cautious)
Introverted <-> Externality (Bold)
LII+EIE HEF <-> Impressionable
ESI+LSE HEF <-> Unimpressionable
LIE+EII HEF <-> Informational
ESE+LSI HEF <-> Energetic
ILE+SLI HEF <-> Tensioned
SEE+IEI HEF <-> Relaxed
IEE+SEI HEF <-> Inhibitable
SLE+ILI HEF <-> Excitable

Detached <-> Inert
Involved <-> Contact
Implicit <-> Weak
Explicit <-> Strong
Alpha <-> Evaluative
Gamma <-> Situational
Delta <-> Unvalued
Beta <-> Valued

SLE Automorphism from elements to positions:

Static <-> Opening (Mental)
Dynamic <-> Closing (Vital)
Irrational <-> Stable (Accepting)
Rational <-> Unstable (Producing)
Extroverted <-> Externality (Bold)
Introverted <-> Internality (Cautious)
LII+EIE HEF <-> Relaxed
ESI+LSE HEF <-> Tensioned
LIE+EII HEF <-> Inhibitable
ESE+LSI HEF <-> Excitable

ILE+SLI HEF <-> Unimpressionable
SEE+IEI HEF <-> Impressionable
IEE+SEI HEF <-> Informational
SLE+ILI HEF <-> Energetic

Detached <-> Contact
Involved <-> Inert
Implicit <-> Weak
Explicit <-> Strong
Alpha <-> Situational
Gamma <-> Evaluative
Delta <-> Unvalued
Beta <-> Valued

IEI Automorphism from elements to positions:

Static <-> Closing (Vital)
Dynamic <-> Opening (Mental)
Irrational <-> Stable (Accepting)
Rational <-> Unstable (Producing)
Extroverted <-> Internality (Cautious)
Introverted <-> Externality (Bold)
LII+EIE HEF <-> Excitable
ESI+LSE HEF <-> Inhibitable
LIE+EII HEF <-> Tensioned
ESE+LSI HEF <-> Relaxed
ILE+SLI HEF <-> Informational
SEE+IEI HEF <-> Energetic
IEE+SEI HEF <-> Unimpressionable
SLE+ILI HEF <-> Impressionable

Detached <-> Inert
Involved <-> Contact
Implicit <-> Strong
Explicit <-> Weak
Alpha <-> Situational
Gamma <-> Evaluative
Delta <-> Unvalued
Beta <-> Valued

SEE Automorphism from elements to positions:

Static <-> Opening (Mental)
Dynamic <-> Closing (Vital)
Irrational <-> Stable (Accepting)
Rational <-> Unstable (Producing)
Extroverted <-> Externality (Bold)
Introverted <-> Internality (Cautious)
LII+EIE HEF <-> Inhibitable
ESI+LSE HEF <-> Excitable
LIE+EII HEF <-> Relaxed
ESE+LSI HEF <-> Tensioned

ILE+SLI HEF <-> Informational
SEE+IEI HEF <-> Energetic
IEE+SEI HEF <-> Unimpressionable
SLE+ILI HEF <-> Impressionable

Detached <-> Weak
Involved <-> Strong
Implicit <-> Contact
Explicit <-> Inert
Alpha <-> Unvalued
Gamma <-> Valued
Delta <-> Situational
Beta <-> Evaluative

ILI Automorphism from elements to positions:

Static <-> Closing (Vital)
Dynamic <-> Opening (Mental)
Irrational <-> Stable (Accepting)
Rational <-> Unstable (Producing)
Extroverted <-> Internality (Cautious)
Introverted <-> Externality (Bold)
LII+EIE HEF <-> Tensioned
ESI+LSE HEF <-> Relaxed
LIE+EII HEF <-> Excitable
ESE+LSI HEF <-> Inhibitable
ILE+SLI HEF <-> Unimpressionable
SEE+IEI HEF <-> Impressionable
IEE+SEI HEF <-> Informational
SLE+ILI HEF <-> Energetic

Detached <-> Strong
Involved <-> Weak
Implicit <-> Inert
Explicit <-> Contact
Alpha <-> Unvalued
Gamma <-> Valued
Delta <-> Situational
Beta <-> Evaluative

LIE Automorphism from elements to positions:

Static <-> Closing (Vital)
Dynamic <-> Opening (Mental)
Irrational <-> Unstable (Producing)
Rational <-> Stable (Accepting)
Extroverted <-> Externality (Bold)
Introverted <-> Internality (Cautious)
LII+EIE HEF <-> Unimpressionable
ESI+LSE HEF <-> Impressionable
LIE+EII HEF <-> Energetic
ESE+LSI HEF <-> Informational
ILE+SLI HEF <-> Tensioned
SEE+IEI HEF <-> Relaxed
IEE+SEI HEF <-> Inhibitable

SLE+ILI HEF <-> Excitable

Detached <-> Strong
Involved <-> Weak
Implicit <-> Contact
Explicit <-> Inert
Alpha <-> Unvalued
Gamma <-> Valued
Delta <-> Evaluative
Beta <-> Situational

ESI Automorphism from elements to positions:

Static <-> Opening (Mental)
Dynamic <-> Closing (Vital)
Irrational <-> Unstable (Producing)
Rational <-> Stable (Accepting)
Extroverted <-> Internality (Cautious)
Introverted <-> Externality (Bold)
LII+EIE HEF <-> Informational
ESI+LSE HEF <-> Energetic
LIE+EII HEF <-> Impressionable
ESE+LSI HEF <-> Unimpressionable
ILE+SLI HEF <-> Inhibitable
SEE+IEI HEF <-> Excitable
IEE+SEI HEF <-> Tensioned
SLE+ILI HEF <-> Relaxed

Detached <-> Weak
Involved <-> Strong
Implicit <-> Inert
Explicit <-> Contact
Alpha <-> Unvalued
Gamma <-> Valued
Delta <-> Evaluative
Beta <-> Situational

LSE Automorphism from elements to positions:

Static <-> Closing (Vital)
Dynamic <-> Opening (Mental)
Irrational <-> Unstable (Producing)
Rational <-> Stable (Accepting)
Extroverted <-> Externality (Bold)
Introverted <-> Internality (Cautious)
LII+EIE HEF <-> Informational
ESI+LSE HEF <-> Energetic
LIE+EII HEF <-> Impressionable
ESE+LSI HEF <-> Unimpressionable
ILE+SLI HEF <-> Excitable
SEE+IEI HEF <-> Inhibitable
IEE+SEI HEF <-> Relaxed

SLE+ILI HEF <-> Tensioned

Detached <-> Inert
Involved <-> Contact
Implicit <-> Weak
Explicit <-> Strong
Alpha <-> Situational
Gamma <-> Evaluative
Delta <-> Valued
Beta <-> Unvalued

EII Automorphism from elements to positions:

Static <-> Opening (Mental)
Dynamic <-> Closing (Vital)
Irrational <-> Unstable (Producing)
Rational <-> Stable (Accepting)
Extroverted <-> Internality (Cautious)
Introverted <-> Externality (Bold)
LII+EIE HEF <-> Unimpressionable
ESI+LSE HEF <-> Impressionable
LIE+EII HEF <-> Energetic
ESE+LSI HEF <-> Informational
ILE+SLI HEF <-> Relaxed
SEE+IEI HEF <-> Tensioned
IEE+SEI HEF <-> Excitable
SLE+ILI HEF <-> Inhibitable

Detached <-> Contact
Involved <-> Inert
Implicit <-> Strong
Explicit <-> Weak
Alpha <-> Situational
Gamma <-> Evaluative
Delta <-> Valued
Beta <-> Unvalued

IEE Automorphism from elements to positions:

Static <-> Opening (Mental)
Dynamic <-> Closing (Vital)
Irrational <-> Stable (Accepting)
Rational <-> Unstable (Producing)
Extroverted <-> Externality (Bold)
Introverted <-> Internality (Cautious)
LII+EIE HEF <-> Tensioned
ESI+LSE HEF <-> Relaxed
LIE+EII HEF <-> Excitable
ESE+LSI HEF <-> Inhibitable

ILE+SLI HEF <-> Impressionable
SEE+IEI HEF <-> Unimpressionable
IEE+SEI HEF <-> Energetic
SLE+ILI HEF <-> Informational

Detached <-> Inert
Involved <-> Contact
Implicit <-> Strong
Explicit <-> Weak
Alpha <-> Evaluative
Gamma <-> Situational
Delta <-> Valued
Beta <-> Unvalued

SLI Automorphism from elements to positions:

Static <-> Closing (Vital)
Dynamic <-> Opening (Mental)
Irrational <-> Stable (Accepting)
Rational <-> Unstable (Producing)
Extroverted <-> Internality (Cautious)
Introverted <-> Externality (Bold)
LII+EIE HEF <-> Inhibitable
ESI+LSE HEF <-> Excitable
LIE+EII HEF <-> Relaxed
ESE+LSI HEF <-> Tensioned
ILE+SLI HEF <-> Energetic
SEE+IEI HEF <-> Informational
IEE+SEI HEF <-> Impressionable
SLE+ILI HEF <-> Unimpressionable

Detached <-> Contact
Involved <-> Inert
Implicit <-> Weak
Explicit <-> Strong
Alpha <-> Evaluative
Gamma <-> Sitiuational
Delta <-> Valued
Beta <-> Unvalued

____________