Problem of the Week

This week's problem was suggested by Nathan Pauli. Many thanks!

Four brothers have a horrible fight and decide to get as far away from each other as humanly possible. Assuming they stay on the surface of the earth (of course) where should they go so as to realize there greatest mutual separation?

Notes:
(1) You need not give exact latitude and longitude, only describe their relative positions on the globe.
(2) There are several reasonable interpretations of the meaning of "greatest mutual separation". Pick one!

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