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Almost all boxes

We have proved so far that every normal box---

• Has loops (It's not normal to be loopless).
• Has a path from one corner back to a corner (Just right and {$\Delta$} and Destinations).

This means that almost every box, in the sense of Lebesgue measure, has these properties. We can go further. Almost every box

• Has an infinite path starting at a corner (Irrationals and Infinite Paths).
• Has a path infinite in both directions (proof in a moment).

In other words, almost every box has every sort of geodesic.

Bi-infinite Geodesics: Almost every box has a geodesic that is infinite in both directions.