Experimental Topology + Analysis
It is commonly accepted, but rarely drawn, that a Mobius band is a once punctured Projective Plane; a Whitehead lock is a twice punctured Projective Plane; a Borromean lock is a thrice punctured Projective Plane. In an experimental work, M. Phillips produced the following diagrams in which he produces the Olympic Chain from the thrice puncture Projective Plane. Either this is a counter-example or a mistake. From either his drawings or your own, determine what is the case.