Reliance on π-diagrams and tangent plots to describe fold geometry has created an unwarranted status for conical folds at the expense of periclines. Analysis of virtual periclines using synthetic stereograms, tangent diagrams, and geologic curvature analysis demonstrates small portions of periclines are "cylindrical." The more significant "non-cylindrical" portion of periclines allows for a mathematically permissible, but unrealistic, geometrical representation as portions of cones. We demonstrate cones are an extremely poor geometric representation of both the virtual periclines and examples of natural non-cylindrical folds. "Conical folds," if they exist, terminate at a point; the amplitude to width ratio and the plunge of the crestal line must remain constant towards the fold terminus, with a Gaussian curvature of zero. In contrast, the amplitude to width ratio, plunge along the crestal line, and Gaussian curvature of periclines vary towards the fold terminus. These differences have important implications for the rheological modeling of folds, and while realistic dynamic models for periclines exist, models for conical fold formation remain conceptual. We suggest that in order to advance our understanding of how folds form, it may be "pointless" to continue the misconception of conical folds as an accurate geometric representation of how folds end.