by wendy » Fri Mar 14, 2014 7:35 am
Plate tectonics in 4d would consist of plates etc, but the fault lines would now be hedrous (ie 2d shaped). As with 3d, there is no reason for the faults to be either singular or connected. A fault is like a fence: it's a division of the surface, and therefore is of dimension S-1. Since here S is driven by gravity, and is N-1, the fault is in 4D, a hedrous form, and the plates, being as faces of a polytope, a chorous form.
Rift faults can still form, but rifts are also a hedrous affair. You would either travel a long way or build a crossing to get across a rift in any space.