A study is made of $R^6$ as a singular quotient of the conical space
$R^+\times CP^3$ with holonomy $G_2$ with respect to an obvious action by
$U(1)$ on $CP^3$ with fixed points. Closed expressions are found for the
induced metric, and for both the curvature and symplectic 2-forms
characterizing the reduction. All these tensors are invariant by a diagonal
action of $SO(3)$ on $R^6$, which can be used effectively to describe the
resulting geometrical features.