Twists on the front and back of the paper are related by more than simply turning the paper over—the transformations in pleats that lead to ever-larger twists eventually lead to twists on the other side of the paper when done in reverse. Given two fixed pleats, these transformations in each shape of grid-based twist produces an evenly spaced line of twist centers, defining the number line of that particular twist shape. Different twist shapes will have different distances between a closed twist on the front of the paper and a closed twist on the back of the paper along this number line depending on the angle between the two fixed pleats. Hybrid twists (ones that combine pleat properties of different sizes of twists of the same shape) have centers that may deviate from this number line. In certain applications of symmetry on certain tilings, the relative locations of twists (on the number line of twists) that occupy distinct tiling positions can be used to predict the twist that will occupy the final tiling position. This is useful for navigating the combinatorial explosion of potential tessellation designs while avoiding the twist(s) on the number line that require precreasing before the final collapse of the pattern. This paper will explore the number lines of square, hexagon, and triangle twists and their use in design equations on the \(4^4\) and \((3.6)^2\) tilings.