Geodesic
Two Examples of Solids Constructed From Given Developments
Journal for geometry and graphics, Tome 20 (2016) no. 2, pp. 225-241.

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

The paper provides two examples, where the bending of a planar area Φ0 with boundary c0 generates a developable surface patch Φ bounded by a particular spatial curve c. There are various ways to restrict such bendings. In the first example the surface Φ is a cylinder with given rulings, and the spatial counterpart c of the boundary c0 is planar. In the second example the rulings are unknown. Instead of this constraint, the closed boundary c0 is subdivided into two subarcs which are glued together while Φ0 is bent. In both examples we obtain solids enclosed by torses with geodesic circles c as curved edges.
Classification : 53A03, 51M04, 51N05, 68U07
Mots-clés : Surfaces of constant curvature, curved folding, developable surfaces, geodesic circle 
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     title = {Two {Examples} of {Solids} {Constructed} {From} {Given} {Developments}},
     journal = {Journal for geometry and graphics},
     pages = {225--241},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2016},
     url = {http://geodesic.mathdoc.fr/item/JGG_2016_20_2_JGG_2016_20_2_a5/}
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H. Stachel . Two Examples of Solids Constructed From Given Developments. Journal for geometry and graphics, Tome 20 (2016) no. 2, pp. 225-241. http://geodesic.mathdoc.fr/item/JGG_2016_20_2_JGG_2016_20_2_a5/