The Crosscap.
It is one of the different
faces of the projective plane. See
article
.
This surface has two "cusp points", or "Whitney umbrellas".
See also the article, to better
understand. The psychoanalyst Jacques Lacan saw in it an image of the "fundamental fantasy" and located "objet a", the "linguistic phallus",
on the central cusp point. See "J.P. Petit with Jacques Lacan".
Penetrate with a little skill
inside the Crosscap to observe from this point of
view the central cusp point and notice that it is identical to
the other.
Polyhedral Version