Intersecting Cylinders with Hollow Middle (AR Modeling Challenge)

The goal of this GeoGebra Augmented Reality modeling challenge is to [b]construct 2 cylinders that intersect, yet have a hollow middle[/b]. [br][br]In the screencast below, each right circular cylinder has radius = 1. The lines that pass through [math]\left(0,0,0\right)[/math] and [math]\left(1,\pm1,0\right)[/math] serve as axes for both these cylinders. [br][br]How can we construct such a surface by authoring only 2 surface equations?
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Information: Intersecting Cylinders with Hollow Middle (AR Modeling Challenge)