Nawratil, G. (2023). Generalizing Continuous Flexible Kokotsakis Belts of the Isogonal Type. In L.-Y. Cheng (Ed.), ICGG 2022 - Proceedings of the 20th International Conference on Geometry and Graphics (pp. 115–126). https://doi.org/10.1007/978-3-031-13588-0_10
A. Kokotsakis studied the following problem in 1932: Given is a rigid closed polygonal line (planar or non-planar), 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 line-segments, 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 so-called 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 so-called V-hedra composed of skew quads. The latter also gives a positive answer to a question posed by R. Sauer in his book of 1970 whether continuous flexible skew quad surfaces exist.
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Project title:
Advanced Computational Design: F77 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF))