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The manifold of planes that intersect four straight lines in points of a circle. (English) Zbl 1081.51501
Summary: Our topic is the manifold of planes that intersect four straight lines in three-dimensional euclidean space in points of a circle. The solution manifold is of class seven and contains 24 single lines, four double lines, a triple plane and four dual conics. We compute the equation of the solution manifold, visualize it and discuss the special case of the four base lines being contained in a regulus.

MSC:
51M05 Euclidean geometries (general) and generalizations
53A04 Curves in Euclidean and related spaces
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