It implies the [Banach-Tarski Paradox][1] ...


  [1]: http://matwbn.icm.edu.pl/ksiazki/fm/fm138/fm13813.pdf " Pawlikowski, Janusz. The Hahn-Banach theorem implies the Banach-Tarski paradox. Fundamenta Mathematicae 138.1 (1991): 21-22"