  Note that in the construction of  Γ1,  i.e. the set of 10 points forming 22 interlocking triples, all points except a9 appear in more than one triple. In  Γ2 every  point appears in a multiplicity of triples. It is here that the noncontextuality premise is crucial to the argument: we assume that an arbitrary point keeps its value 1 or 0 as we move from one orthogonal triple to the next (i.e. from one maximal set of compatible observables to another).