“Discussion of the subject of relating is a much easier exercise for analysts than is the discussion of usage, since relating may be examined as a phenomenon of the subject, and psychoanalysis always likes to be able to eliminate all factors that are environmental, except in so far as the environment can be thought of in terms of projective mechanisms. But in examining usage there is no escape: the analyst must take into account the nature of the object, not as a projection, but as a thing in itself.” 
The quadripod provides a way of distinguishing Freud’s third form of identification to object-as-symptom in Group Psychology, summarised as follows:
Some of the consequences of this can be seen in the different relation to the thing-in-itself as formulated by Bion in comparison with that formulated by the Lacanian reading of Freud. Bion, in contrast to Freud, placed the contact barrier between the unconscious and the conscious, with the container-contained dialectic being progressively transformed through the work of analysis from a paranoid-schizoid to a depressive relation to the unconscious. This transformation of the relation between secondary and primary process enabled the individual to know something of the thing-in-itself (Bion’s relation to ‘O’) by coming to be able to experience primary process ‘without memory and without desire’, under which conditions the knower’s relation to the thing-in-itself could be symmetric:
We can contrast this with Lacan’s formulation in which this relation between the conscious and unconscious is orthogonal to the axis along which the relation to the thing-in-itself is experienced as the relation to the ‘lack’ qua desire. This Thus while the end of analysis in Bion’s terms was to be able to take up a relation to ‘O’, almost in the sense of a zen master, for Lacan the end of analysis was for the individual to be able to take up their particular symptom and live ‘true to desire’ – the individual’s particular way of being in relation to lack. What was at stake here in Lacan’s terms was the nature of the third identification to the symptom, transformed by analysis into chthonic destiny qua sinthome.
Why make this yang/yin distinction? Because without it, it is difficult to understand the between-two-deaths ethical good lying beyond the sovereign good in the Platonic ideal underpinning Bion’s ‘O’.
 My italics. The quote is from Winnicott, D. W. (1969). “The use of an object.” International Journal of Psychoanalysis 50: 711-716.
 This formulation by Bion differed from Freud’s. Bion placed the contact barrier between the unconscious (aka the pre-conscious/protomental) and the conscious, with the container-contained alpha-functioning progressively transforming the relation to the unconscious (See Bion’s Learning from Experience p17ff). This understanding of the contact-barrier differed from Freud’s, for whom the neuronal contact barriers distributed quantities of affect generated by experiencing (whether endogenous or exogenous) through a process of complexification with their entangled qualities. The distinction Freud made in his Project was between the pre-conscious and the radically unconscious, and was between the complexification of thing-presentation in the -complex and word-presentation in the -system. It is this more complex reading of the relationship between the conscious and the unconscious that is taken up by Lacan.
 The ways in which we are linked to nature through being embodied. In this sense, the quadripod is a way of thinking about the relationship between identity and the processes of identification.