In this paper we consider configurations of straight lines in general position in a plane with all intersection points marked to show which of the two lines is “above” the other. We prove that there exist two isotopic configurations such that one of them can be obtained as a projection of a collection of straight lines in 3-space, and the other not. We investigate some isotopism class of configurations of six lines and find a necessary and sufficient condition for configurations from this class to be a projection of a collection of lines in 3-space.
Mathematics Subject Classification (2000):Primary 51M20
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