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The cross-cap, or more precisely, the projective plane, can [[represent ]] the subject of [[desire ]] in relation to the lost [[object]]. A [[double ]] loop drawn on its surface in effect [[divides ]] this single-sided surface into two heterogeneous parts: a Möbius [[strip ]] representing the subject and a disk representing [[object a]], the [[cause ]] of desire. The disk is centered on a point that is related to the irreducible singularity of this surface, which [[Lacan ]] [[identified ]] with the [[phallus]]. Unlike the [[representation ]] of the subject produced on the torus, here a single cut, which symbolizes [[castration]], produces both the subject and the object in its divisions ([[figure ]] 7).