I suspect they've spent much longer looking at 2d shapes than 3d ones (because they're easier to imagine and reason about, and there are fewer variations in how "aperiodic monotile" can be defined in 2d).
Also, the tricky bit for this kind of shape (similarly to Penrose's tiles) isn't finding the shape, but finding the aperiodic tiling and adding gadgets that rule out any periodic tilings (and proving this). The actual aperiodic monotile shown looks like it has 201 faces (although that could trivially be reduced by quite a bit).
> However, the paper itself and the formalization that it claims for support are not
in a form that is readily usable to anyone who wants to understand or check it. This is
not just because of the needless length or complexity of the argument (which is indeed
overwhelming as presented), or because the formal repository is not in normal form, or
because much of the text is misleading or poorly organized, but mainly because there
is so much irrelevant puff to push through.
Also, the tricky bit for this kind of shape (similarly to Penrose's tiles) isn't finding the shape, but finding the aperiodic tiling and adding gadgets that rule out any periodic tilings (and proving this). The actual aperiodic monotile shown looks like it has 201 faces (although that could trivially be reduced by quite a bit).
Zing