Triskel

The "triskel" in Lacan's Seminar 22 names the three-ring pre-Borromean configuration of the Symbolic, Imaginary, and Real considered as a figure in its own right — a triskele, the three-armed rotating form — before or without the intervention of a fourth knotting term. Lacan mobilizes this term to mark the structural insufficiency of the triadic RSI arrangement on its own: left to itself, the triskel's three rings do not form a genuine Borromean chain in the clinical sense required for a subject to hold together. The Name-of-the-Father must intervene as a "buckle" — a fourth ring that loops around and through the three to convert a mere figure of three into an effective Borromean bond. The triskel is thus not the Borromean Knot but its topological precondition and limit: the three-part arrangement that needs supplementation.

This move is decisive because it introduces an asymmetry into the RSI structure: rather than three equivalent rings in mutual dependence, the triskel functions as the base upon which the paternal fourth term operates. In the context of Freud's three identifications (with an object, with a unary trait, via a shared situation of desire), the triskel maps the three axes — love, identification, desire — while the Name-of-the-Father supplies the knotting that holds all three axes in social and subjective coherence. The cartel's "three plus one" structure is thus grounded topologically in this exact architecture: three (the triskel) plus the fourth term (the Name-of-the-Father as buckle).

The concept lives in jacques-lacan-seminar-22 and belongs squarely to Lacan's late topological period, in which the Borromean Knot becomes the primary formal apparatus for thinking the RSI triad. The triskel is best understood as a specification internal to the Borromean Knot framework: it names the three-ring figure in its potentially unbound state, foregrounding its dependence on the Name-of-the-Father as the fourth knotting element. This directly extends the Borromean Knot's principle — that no two rings are intrinsically linked, and that the structure's coherence is always a third-term (or fourth-term) effect — by giving the three-ring configuration its own name and marking it as structurally incomplete without supplementation.

The triskel also crystallizes the intersection of several cross-referenced canonicals. Identification (particularly the unary trait / einziger Zug) appears explicitly in the passage as the mode of inscription that anchors the triskel's Symbolic ring. The Name-of-the-Father, as the fourth-ring buckle, performs the function Lacan elsewhere assigns to the sinthome in Seminar XXIII — both are supplementary terms that repair or complete a knotting that the three registers cannot achieve alone. The Imaginary's property of consistency (its role in the knot's three-dimensionality) and the Symbolic's hole are implicitly at stake in distinguishing the triskel's three arms. And the claim that "there is only love because of the fact that the Name-of-the-Father makes a buckle" connects the triskel directly to Desire and to the social bond: the cartel's structure of three-plus-one is the institutional form of a topology already inscribed in the knot itself.

Seminar XXII · R.S.I.Jacques Lacan · 1974 (p.168)

It is only inscribed from consistency, he called that the unary trait, one could not say better! Which is a component of the knot, not without having got the idea that there is only love, I would say, because of the fact that the Name-of-the-Father makes a buckle between the three, makes a buckle of the three of the triskel.

The phrase "makes a buckle of the three of the triskel" is theoretically loaded because it names both the insufficiency of the three-ring figure and its remedy in a single movement: "buckle" (boucle) designates precisely the topological operation by which the Name-of-the-Father loops through and around the three rings, converting the triskel's open or merely figural three-ness into a closed, holding Borromean bond. The prior phrase anchors this in identification theory — "consistency" is the Imaginary's topological property, and the "unary trait" is the mark of symbolic identification — showing that the triskel's three arms are already mapped onto the three registers and the three modes of Freudian identification that the buckle must knot together.