Voderberg tiling

Voderberg, his student, answered in the affirmative with Form eines Neunecks eine Lösung zu einem Problem von Reinhardt ["On a nonagon as a solution to a problem of Reinhardt"].

[2][3] It is a monohedral tiling: it consists only of one shape that tessellates the plane with congruent copies of itself.

In this case, the prototile is an elongated irregular nonagon, or nine-sided figure.

E.g., the lowest purple nonagon is enclosed by two yellow ones, all three of identical shape.

Because it has no translational symmetries, the Voderberg tiling is technically non-periodic, even though it exhibits an obvious repeating pattern.