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.
"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.