Geodesic
The Extended Oloid and Its Contacting Quadrics
Journal for geometry and graphics, Tome 19 (2015) no. 2, pp. 161-177.

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The oloid is the convex hull of two circles with equal radius in perpendicular planes so that the center of each circle lies on the other circle. It is part of a developable surface which we call extended oloid. We determine the tangential system of all contacting quadrics Q of the extended oloid O. From this result we conclude parameter equations of the touching curve c between O and Q, and of the edge of regression of O. Properties of the curves c are investigated. The self-polar tetrahedron of the tangential system of quadrics is obtained. The common generating lines of O and any ruled surface Q are determined. Furthermore, we derive the curves which are the images of c when O is developed onto the plane.
Classification : 53A05, 51N20, 51N15
Mots-clés : Oloid, developable surface, torse, tangential system of quadrics, touching curve, edge of regression, self-polar tetrahedron, ruled surface 
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U. B�sel; H. Dirnb�ck . The Extended Oloid and Its Contacting Quadrics. Journal for geometry and graphics, Tome 19 (2015) no. 2, pp. 161-177. http://geodesic.mathdoc.fr/item/JGG_2015_19_2_JGG_2015_19_2_a0/