Abstract
We show that for every n > 0 there is a planar topological disk A0 and n translates A1, A2, ..., An of A0 such that the interiors of A0, ..., An are pairwise disjoint, but with each Ai touching A0 for 1 ≤ i ≤ n.
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Cheong, O., Lee, M. The Hadwiger Number of Jordan Regions Is Unbounded. Discrete Comput Geom 37, 497–501 (2007). https://doi.org/10.1007/s00454-007-1346-3
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DOI: https://doi.org/10.1007/s00454-007-1346-3