Geodesic
Closed Space Curves Made from Circles on Polyhedra
Journal for geometry and graphics, Tome 15 (2011) no. 1, pp. 29-43 Cet article a éte moissonné depuis la source Heldermann Verlag

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Suppose that P is a polyhedron, all of whose faces are regular polygons such that the incircles of adjoined faces are tangent to each other. Various closed space curves are then determined by linking together portions of the circles. This paper examines such biarc curves, concentrating on those which lie not only on P, but also on a sphere. Thirteen of these are called the regular polyhedral polyarcs: two on a tetrahedron, three on a cube, two on an octahedron, four on a dodecahedron, and two on an icosahedron. More general spherical circle-to-circle curves are also considered.
Classification : 51M20, 51M04, 51N20
Mots-clés : biarc, polyarc, regular polyhedra, sphericon, spherical curve, quadrarc 
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     author = {C. Kimberling and P. J. C. Moses },
     title = {Closed {Space} {Curves} {Made} from {Circles} on {Polyhedra}},
     journal = {Journal for geometry and graphics},
     pages = {29--43},
     year = {2011},
     volume = {15},
     number = {1},
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C. Kimberling; P. J. C. Moses . Closed Space Curves Made from Circles on Polyhedra. Journal for geometry and graphics, Tome 15 (2011) no. 1, pp. 29-43. http://geodesic.mathdoc.fr/item/JGG_2011_15_1_JGG_2011_15_1_a2/