Apparently, mattress flipping is an applied mathematics concept. I didn’t realize it can be that complicated. But in an article written on American Scientist, flipping a mattress involves a “mythical combination (which is) a mathematical ‘golden rule’”.
Mathematically, there are four ways to rotate a mattress so that it ends up aligned with the bed. Hayes uses the symbols I for the Identity rotation and R, P, Y for the nautical terms Roll, Pitch and Yaw. No matter how creatively you manipulate your mattress, once it’s back on the bed you will have performed one of the four operations I, R, P, Y shown in the figure. Each of these operations has the property that if you repeat it, you end up where you started. So you will have missed two of the configurations.
Huh? 
via The Sum
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