Geometric permutations of non-overlapping unit balls revisited

@article{Ha2016GeometricPO,
title={Geometric permutations of non-overlapping unit balls revisited},
author={J. Ha and O. Cheong and X. Goaoc and Jungwoo Yang},
journal={Comput. Geom.},
year={2016},
volume={53},
pages={36-50}
}

Given four congruent balls A , B , C , D in R ? that have disjoint interior and admit a line that intersects them in the order ABCD, we show that the distance between the centers of consecutive balls is smaller than the distance between the centers of A and D. This allows us to give a new short proof that n interior-disjoint congruent balls admit at most three geometric permutations, two if n ? 7 . We also make a conjecture that would imply that n ? 4 such balls admit at most two geometricâ€¦Â CONTINUE READING