Thursday, April 10, 2025

[dliiohsn] hexagons in a rectangle

what rectangle aspect ratios permit finite tessellations of regular hexagons to be neatly inscribed within them?

assuming one edge of hexagons parallel to one edge of rectangle, this should be easy.  in other words, close-packed clusters of regular hexagons circumscribed by a rectangle, two (opposite) sides of the rectangle coincident with edges of outermost hexagons, and the two other (opposite) sides of the rectangle coincident with outermost hexagon vertices.

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