3 ms·

As I understand it: they found a single shape. Where existing Penrose tilings were composed of two (or more) shapes.

• phkahler 4y ago
  But in one sense this is actually 2 shapes that are mirror images. It's still really cool, but I don't think it is ultimately what we've been looking for. As proof that it's not, we all know that a paper presenting one that doesn't need its mirror image to tile the plane aperiodically would still be a big dea.
• pohl 4y ago
  ...they found a single shape Kind of, though, right? One could also look at it as they've found two shapes that happen to be reflections of each other.
  • Jarmsy 4y ago
    Rigid transformations of a single shape https://en.wikipedia.org/wiki/Rigid_transformation https://en.wikipedia.org/wiki/Rigid_transformation
• dekhn 4y ago
  It's not really a single shape since the tiling contains the shape's reflection which is normally considered a different shape since its handedness changes.