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Where, exactly, are the barreloids? Perceptually the cube is bistable, a Necker cube the solid lines either representing the cube's front face or back face. It could drive an anatomist crazy! (Note: 'L' stands for 'lateral' and 'R' stands for 'rostral').
While the figure is perceptually ambiguous, it is clear from the paper that they follow the convention that solid lines are to be interpreted as in the front. Also, based on an informal poll of people in my lab, it seems most people lock in on the "correct" perceptual interpretation initially.