The binary tetrahedral group \(2T\) is small enough for explicit
calculations, yet it connects finite symmetry, representations, real Group
Algebras, and the quaternionic structures familiar from spin mathematics.
Its concrete realization by Hurwitz units, and their identification with
\(2T\), are described in
[voight2021quaternion, sec. 11.2, pp. 166--168], while the relation
between representations and Group-Algebra modules is developed in
[sengupta2010representations, secs. 3.1--3.3, pp. 39--42]. Wilson uses
order-3 automorphisms of \(Q_8\) to discuss possible physical
interpretations in
[wilson2021finite, sec. 4.3, pp. 12--13, v5]. He later adjoins an
abstract generator \(f\) of order 3 to \(Q_8\) to form \(2T\) in
[wilson2021finite, sec. 6.1, p. 18, v5].
Any physical identification remains a hypothesis. A proposed
correspondence must specify an action and representation, an algebra map, any
preserved structure or form, a unit-group choice where applicable, and the
intended physical meaning. Resemblance alone is not a model.