A novel representation of spin 1/2 combines in a single geometric object the roles of the standard
Pauli spin vector operator and spin state. Under the spin-position decoupling approximation it consists of
three orthonormal vectors comprising a gauge phase. In the one-particle case the representation: (1) is
Hermitian; (2) shows handedness; (3) reproduces all standard expectation values, including the total one particle
spin modulus 𝑆tot = √3ℏ/2; (4) constrains basis opposite spins to have same handedness; (5)
allows to formalize irreversibility in spin measurement. In the two-particle case: (1) entangled pairs have
precisely related gauge phases and can be of same or opposite handedness; (2) the dimensionality of the spin
space doubles due to variation of handedness; (3) the four maximally entangled states are naturally defined
by the four improper rotations in 3D: reflections onto the three orthogonal frame planes (triplets) and
inversion (singlet). The cross-product terms in the expression for the squared total spin of two particles
relates to experiment and they yield all standard expectation values after measurement. Here spin is directly
defined and transformed in 3D orientation space, without use of eigen algebra and tensor product as in the
standard formulation. The formalism allows working with whole geometric objects instead of only
components, thereby helping keep a clear geometric picture of ‘on paper’ (controlled gauge phase) and ‘on
lab’ (uncontrolled gauge phase) spin transformations.