  It is shown that a simple graph which is embeddable in the real projective
plane is minimally 3-rigid if and only if it is (3,6)-tight. Moreover the
topologically uncontractible embedded graphs of this type are constructible
from one of 8 embedded graphs by a sequence of vertex splitting moves. In
particular the characterisation of minimal 3-rigidity holds for a triangulated
Mobius strip.
