“No such thing,” you say, since you are a knowledgeable geometer.
I first saw the phrase “hexagonal squares” when I was 13 or 14, reading the instruction manual for an Avalon Hill board game (probably the second or so incarnation of Gettysburg, if memory serves). Yes, even then I was a reader of instruction manuals. As a budding linguist with a deep interest in math, I was startled by the inappropriate phrase “hexagonal squares,” though fortunately the manual did point out “hex” as a convenient shortcut. I don’t play board games anymore, but I believe that “hex” is still the term of art.
We can ignore the inapposite use of the word “squares”; the real question, of course, is “Why hexagons?”
Well, because “hexagons are the bestagons,” in the words of CGP Grey (more from him in a later post). Do watch this video, which comes in in less than (not “fewer than,” no matter what you might think) ten minutes; it’s informative, entertaining, and not too heavy. And then you can ponder deep philosophical questions like “How do bees know to make hexagonal cells for their wax?“ and “How does Saturn know to place a hexagonal pattern atop its north pole?“ Inquiring minds want to know.