There's at least one more distinct set of dry-land points, in Canada, Chile, Kenya, and Australia, which was found by Gram Zeppi in a Quora answer: https://www.

There's at least one more distinct set of dry-land points, in Canada, Chile, Kenya, and Australia, which was found by Gram Zeppi in a Quora answer: https://www.quora.com/How-can-we-determine-whether-there-are-four-points-on-dry-land-forming-a-regular-tetrahedron-inscribed-in-the-Earth https://www.quora.com/How-can-we-determine-whether-there-are... . An approximate map, using Nairobi, Santiago, Brisbane, and Yellowknife (Canada) as the points: http://www.gcmap.com/mapui?P=nbo-scl-bne-nbo,+yzf-nbo,+yzf-scl,+yzf-bne http://www.gcmap.com/mapui?P=nbo-scl-bne-nbo,+yzf-nbo,+yzf-s... . (My interest is a bit different from Barr's, in that I'm trying to get the points to be near civilization, not far from it.)