Suppose there are two distinct tetrahedral cones in $\mathbb{R}^{3}$ with vertices at the origin. Each cone is formed by three rays emanating from the origin.
(i) Is it possible to project (orthogonally) onto some face of at least one cone from any point outside the cones ?
(ii) If so, how can you divide the space outside the given cones into further cones so that any point therein is projected onto some face of exactly one or both given cones ?
What geometrical features are required to characterize the above situations ?