In June 2011, after looking at an earlier version of this website, the artist-mathematician Robert Fathauer sent me eleven new tilings extended from the "forbidden" vertex figures.

Not only do these tilings often have smaller translational units than the tilings extended from these vertex figures elsewhere on this site, but seven of them are nutshell tilings!

I've described these tilings on the pages below using the same format I've used for the rest of this site.

While Robert discovered these tilings, he has stressed to me that he hasn't made an exhaustive search to determine if they had been found previously by others. In particular, the 3.9.18 Art tiling, or at least related tilings, appear in Islamic art.

It is wonderful to get more examples of tilings extended from the "forbidden" vertex figures - the more examples we find, the more likely it is that we may find beautiful patterns and perhaps new mathematics.

I'd welcome more such tilings extended from the 3.7.42, 3.8.24, 3.9.18, 3.10.15, 4.5.20 or 5.5.10 vertex figures. Please send descriptions to kevinjardine at yahoo dot com.