Abstract
A finite planar set is k-isosceles for k ≥ 3 if every k-point subset of the set contains a point equidistant from the other two. In [1] Fishburn obtains several important results about isosceles planar sets and poses a series of conjectures and open questions. We disprove Conjecture 1 in [1] and provide another 34 nonsimilar 4-isosceles 8-point planar sets which answer one of the open questions in [1] negatively.
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Xu, C., Ding, R. More About 4-Isosceles Planar Sets. Discrete Comput Geom 31, 655–663 (2004). https://doi.org/10.1007/s00454-003-0825-4
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DOI: https://doi.org/10.1007/s00454-003-0825-4