ABSTRACT
This chapter explores several interesting variations of the simple flat twists. In the thin-flange version, there are two possible configurations: one layer continues straight, the other is folded, and depending on which is which, the flange points left or right, as shown on the left and in the middle. Once folded, the thick-flange structures are distinctly different from their thin-flange brethren. After working out the mathematics for thin-flange, thick-flange, and generalized-flange patterns, with both azimuthal and axial unfoldings, the field seemed like it had been thoroughly plowed. In the thin-flange algorithm, all of the excess paper outside of the gores is gathered into either a clockwise- or counterclockwise-pointing flange. In the thick-flange algorithm, the excess paper is divided symmetrically between two flanges that point in opposite directions. Many origami artists have come to explore the concept of rotationally symmetric solids.
