Geodesic
On Continuous Flexible Kokotsakis Belts of the Isogonal Type and V-Hedra with Skew Faces
Journal for geometry and graphics, Tome 26 (2022) no. 2, pp. 237-251 Cet article a éte moissonné depuis la source Heldermann Verlag

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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-hedron 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.
Classification : 51N55, 51M04, 51N15
Mots-clés : Kokotsakis belt, continuous flexibility, skew quad surface 
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     author = {G. Nawratil },
     title = {On {Continuous} {Flexible} {Kokotsakis} {Belts} of the {Isogonal} {Type} and {V-Hedra} with {Skew} {Faces}},
     journal = {Journal for geometry and graphics},
     pages = {237--251},
     year = {2022},
     volume = {26},
     number = {2},
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G. Nawratil . On Continuous Flexible Kokotsakis Belts of the Isogonal Type and V-Hedra with Skew Faces. Journal for geometry and graphics, Tome 26 (2022) no. 2, pp. 237-251. http://geodesic.mathdoc.fr/item/JGG_2022_26_2_JGG_2022_26_2_a3/