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A figure with Heesch number 6: Pushing a two-decade-old boundary, Bojan Bašić, Mathematical Intelligencer, https://doi.org/10.1007/s00283-020-10034-w

When a shape cannot tile the plane, its Heesch number (https://en.wikipedia.org/wiki/Heesch%27s_problem) measures how far you can tile before getting stuck: if you surround the shape by layers of the same shape, how many layers can you make? Casey Mann's previous record, 5 looked like a row of five hexagons with extra crenellations. This one uses six hexagons, with simpler crenellations.