I asked Professor Grunbaum about "Petra" and her tile, and he gave me the following information:
"Petra" is Petra Gummelt, of Greifswald.
Her tile is based on the "Cartwheel decagon", which Professor Conway proved cover every Penrose triangle tiling (Grunbaum & Shephard, p. 559). As I understand it, she colors the cartwheel in such a way that when colored regions overlap exactly a Penrose tiling is generated.
So, the decagons don't really tile the plane. They overlap according to some matching rules, and the resulting planar pattern is aperiodic.
It seems that the work was motivated by questions about the atomic structure of "quasicrystals" of aluminum alloys.
I hope she will join the list and comment on this in person.