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We construct an edge-weight distribution for i.i.d. first-passage percolationon $\mathbb{Z}^2$ whose limit shape is not a polygon and whose extreme pointsare arbitrarily dense in the boundary. Consequently, the associatedRichardson-type growth model can support coexistence of a countably infinitenumber of distinct species, and the graph of infection has infinitely manyends.

Examples of nonpolygonal limit shapes in i.i.d. first-passage percolation and infinite coexistence in spatial growth models