
Journal for Geometry and Graphics 26 (2022), No. 2, 237251 Copyright Heldermann Verlag 2022 On Continuous Flexible Kokotsakis Belts of the Isogonal Type and VHedra with Skew Faces Georg Nawratil Vienna University of Technology, Vienna, Austria nawratil@geometrie.tuwien.ac.at A. Kokotsakis studied the following problem in 1932: Given is a rigid closed polygonal line (planar or nonplanar), which is surrounded by a polyhedral strip, where at each polygon vertex three faces meet. Determine the geometries of these closed strips with a continuous mobility. On the one side, we generalize this problem by allowing the faces, which are adjacent to polygon linesegments, to be skew; i.e to be non planar. But on the other side, we restrict to the case where the four angles associated with each polygon vertex fulfill the socalled isogonality condition that both pairs of opposite angles are equal or supplementary. In more detail, we study the case where the polygonal line is a skew quad, as this corresponds to a (3 × 3) building block of a socalled Vhedron composed of skew quads. The latter also gives a partial answer to a question posed by R. Sauer in his book of 1970 whether continuous flexible skew quad surfaces exist. Keywords: Kokotsakis belt, continuous flexibility, skew quad surface. MSC: 51N55; 51M04, 51N15 [ Fulltextpdf (2554 KB)] 