This is inspired by another tiling from Annie Perkins, https://twitter.com/Anniekperkins/status/983839592204906497. Paula Beardell Krieg posted a precisely made version, https://twitter.com/PaulaKrieg/status/986688492821508097, that made me finally make an applet to play with the symmetry for any quadrilateral. (And educated me as to a proper name for it.) It turns out that you can make several different classic tilings.