a scalar coming from the extra dimensional part of the gauge fields. This scalar VEV must also comply with the boundary conditions coming from orbifolding. Therefore when applying both mechanisms of breaking the symmetry, the VEVs coming from the Wilson Line must lie in the rank-breaking direction of the scalar with the zero mode, thereby breaking the rank of the gauge group [^5]. We emphasise that the orbifold breaking alone does not reduce the rank of the gauge group. With both orbifold and Wilson line breaking, the VEV must be aligned along the rank breaking direction, thereby reducing the rank of the remaining gauge group.

$SO(3)$ Gauge-Flavon Unification {#so3}
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As a first example of the preceding formalism, consider the gauge group $SO(3)$ in 5d, with an orbifold $S^1/Z_2$, where the extra dimensional part of the gauge fields are scalars which transform as triplets under $SO(3)$. If this is chosen to be a gauged family symmetry, these fields are identified as flavons.

The VEVs of such flavons can be achieved via the Wilson line mechanism as described in Section \[Wilson5d\]. We would have as many flavons as extra dimensions (in this case one) and their alignment is fixed by the 