Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 46, No. 2, pp. 435-446 (2005)

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The Intersection Conics of Six Straight Lines

Hans-Peter Schröcker

Institute of Engineering Mathematics, Geometry and Informatics, Innsbruck University, e-mail:

Abstract: We investigate and visualize the manifold $M$ of planes that intersect six straight lines of real projective three space in points of a conic section. It is dual to the apex-locus of the cones of second order that have six given tangents. In general $M$ is algebraic of dimension two and class eight. It has 30 single and six double lines. We consider special cases, derive an algebraic equation of the manifold and give an efficient algorithm for the computation of solution planes.

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Electronic version published on: 18 Oct 2005. This page was last modified: 29 Dec 2008.

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