Abstract
LetM(h, k) denote the topological space whose points are the sets composed ofh lines andk points of ℝ3 in general position. We say thatf∈M(h, k) is mirror if a path exists inM(h, k) that joinsf and its mirror image after reflection in any plane of ℝ3. In this paper we are principally concerned about the following problem (an affine version of a problem proposed by Viro for the projective space): Givenh, k≥0, does somef∈M(h, k) exist such thatf is mirror? This question is solved for all cases except whenh≡1 (mod 4) withh≥5 andk=2 or 3.
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This research was partially supported by DGICYT PB89-0201. This work was done while the author was visiting the University of Liverpool.
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Borobia, A. Mirror property for nonsingular mixed configurations of lines and points in ℝ3. Discrete Comput Geom 11, 311–320 (1994). https://doi.org/10.1007/BF02574011
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DOI: https://doi.org/10.1007/BF02574011