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In the traditional formalism of quantum mechanics, a simple direct proof of(a version of) the Spin Geometry Theorem of Penrose is given; and the structureof a model of the `space of the quantum directions', defined in terms ofelementary $SU(2)$-invariant observables of the quantum mechanical systems, issketched.

A note on Penrose's Spin-Geometry Theorem and the geometry of `empirical quantum angles'