A P-graph is a simple graph G which is embeddable in the real projective plane P. A (3,6)-tight P-graph is shown to be constructible from one of 8 uncontractible P-graphs by a sequence of vertex splitting moves. Also it is shown that a P-graph is minimally generically 3-rigid if and only if it is (3,6)-tight. In particular this characterisation holds for graphs that are embeddable in the M{o}bius strip.
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