Borromean rays and hyperplanes

Three disjoint rays in euclidean 3-space form Borromean rays provided their union is knotted, but the union of any two components is unknotted. We construct infinitely many Borromean rays, uncountably many of which are pairwise inequivalent. We obtain uncountably many Borromean hyperplanes.
Comment: 41 pages, 30 figures (19 with captions, 11 inline)