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Many of these types are basically combining two pentagons into an octagon (or even hexagon) then tiling it across the plane. For some reason, intuitively those seem more easy to me (2 * 3, 2 * 4), so that you could just generate a bunch of them, and split them in two to create tessellating pentagons?

Even the example in the article can be viewed as a regularly tessellating nonagon. I don't see what's "irregular" about it? The article doesn't mention that word, but the HN title does.

"then tiling it across the plane": see https://news.ycombinator.com/item?id=10046349.

"just generate a bunch of them, and split them in two"

Try splitting a 'random' polygon into a set of identical convex (regular or irregular) pentagons.

"what's "irregular" about it?": this has been answered, but for completeness: the sides and angles of the pentagons aren't all identical.

irregular - with sides of different sizes


Sides and/or angles. It's possible to have all the sides the same length, and yet still not be regular. Similarly, it's possible to have all the angles the same, and yet still not be regular. It is instructive to construct examples of both types of failure.

Ah true. A lozenge has all sides with the same size but not the same angles

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