Voderberg tiling

The Voderberg tiling is a mathematical spiral tiling, invented in 1936 by mathematician Heinz Voderberg (1911-1945).[1] It is a monohedral tiling: it consists of only 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. The most interesting feature of this polygon is the fact that two copies of it can fully enclose a third one. E.g., the lowest purple nonagon is enclosed by two yellow ones, all three of identical shape.[2] Before Voderberg's discovery, mathematicians had questioned whether this could be possible.

A partial Voderberg tiling. Note that all of the colored tiles are congruent.

Because it has no translational symmetries, the Voderberg tiling is technically non-periodic, even though it exhibits an obvious repeating pattern. This tiling was the first spiral tiling to be devised,[3] preceding later work by Branko Grünbaum and Geoffrey C. Shephard in the 1970s.[1] A spiral tiling is depicted on the cover of Grünbaum and Shephard's 1987 book Tilings and Patterns.[4]

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