Voderberg tiling

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

The Voderberg tiling is a mathematical spiral tiling, invented in 1936 by mathematician Heinz Voderberg.^[1] It is a monohedral tiling, meaning that it consists of only one shape, tessellated with congruent copies of itself. In this case, the prototile is an elongated irregular enneagon, or nine-sided figure. 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,^[2] preceding later work by Branko Grünbaum and Geoffrey C. Shephard in the 1970s.^[1] A Voderberg tiling is depicted on the cover of Grünbaum and Shephard's 1987 book Tilings and Patterns.^[3]

References

1. Pickover, Clifford A. (2009). The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics. Sterling Publishing Company, Inc. p. 372. ISBN 9781402757969. Retrieved 24 March 2015.
2. Dutch, Steven (29 July 1999). "Some Special Radial and Spiral Tilings". University of Wisconsin, Green Bay. Retrieved 24 March 2015.
3. Grünbaum, Branko; Shephard, G. C. (1987), Tilings and Patterns, New York: W. H. Freeman, Section 9.5, "Spiral Tilings," p. 512, ISBN 0-7167-1193-1.