Two Hexagons from A4 Minus Square — Improved Method

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A while ago I published a post on cutting two hexagons from the rectangle left over after cutting a square from an A4 sheet. For some strange reason, in that original approach, I constructed the two hexagons at the two ends of the long rectangle. A method which seems obviously better is to just prolong the outer edges of the first hexagon, and to continue creasing at 60° angles until a second hexagon is constructed. This approach makes both creasing and cutting faster since some creases are shared between both hexagons.

The hexagons end up exactly the same size as in the older method, and thus the efficiency (proportion of paper area used by the hexagons relative to the whole rectangle) is the same at roughly 92%. The method works for any silver rectangle, of course, and also for other rectangles whose proportions are not too far away from √2:1. Most of the time, I use it with A4 format, cutting a square to fold some model cleanly, and then using the two small hexagons for drafts and experimentation. Either way, it’s always a pity to throw away paper that could still be used for origami, and the process shown here makes it possible to reuse most of the leftovers.