Geodesic
Polyhedral Cylinders Formed by Kokotsakis Meshes
Journal for geometry and graphics, Tome 25 (2021) no. 2, pp. 171-186.

Voir la notice de l'article provenant de la source Heldermann Verlag

Kokotsakis proved that an infinite planar mesh composed of congruent convex, non-trapezoidal, non-parallelogramic quadrilaterals is deformable with degree of freedom 1 in two modes if the quadrilaterals are rigid and if the edges are revolute joints. Stachel proved that in the deformed state the vertices of all quadrilaterals are located on a circular cylinder the radius of which is a free parameter. In other words: A Kokotsakis mesh forms two polyhedral cylinders which are deformable with degree of freedom one. Later, Stachel also investigated under which conditions a polyhedral cylinder is tiled by quadrilaterals. In the present paper new proofs and new results are obtained by using special parameters for quadrilaterals in combination with cylinder coordinates.
Classification : 52C25, 51M20, 70B15
Mots-clés : Kokotsakis mesh, spherical four-bar, polyhedral cylinder, foldable and self-intersecting tiled polyhedral cylinder, periodic polyhedral cylinder, deltoid, parabola through four points 
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     author = {J. Wittenburg },
     title = {Polyhedral {Cylinders} {Formed} by {Kokotsakis} {Meshes}},
     journal = {Journal for geometry and graphics},
     pages = {171--186},
     publisher = {mathdoc},
     volume = {25},
     number = {2},
     year = {2021},
     url = {http://geodesic.mathdoc.fr/item/JGG_2021_25_2_JGG_2021_25_2_a1/}
}
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J. Wittenburg . Polyhedral Cylinders Formed by Kokotsakis Meshes. Journal for geometry and graphics, Tome 25 (2021) no. 2, pp. 171-186. http://geodesic.mathdoc.fr/item/JGG_2021_25_2_JGG_2021_25_2_a1/