Bulge Head: a strangely round volume.

thingiverse

This model shows the volume above the xy-plane, outside of a unit sphere and inside the cardioid of revolution Rho=1+Cos(Phi) (in spherical coordinates). A classic Multivariable Calculus problem asks you to find the volume of the solid. (Of course, using spherical coordinates is the easiest way to solve the problem.) Equivalently, the region in the xy-plane above the y-axis, outside the unit circle, and inside the cardioid r=1+Cos(Theta) (in polar coordinates) is revolved around the y-axis, creating the "bulge head" volume of revolution. This object was designed and printed by my WLU summer research student Ryan McDonnell ('17). You can find more details about this model here: http://mathvis.academic.wlu.edu/2015/07/21/bulge-head-solid/