Voderberg tiling

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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 [de].[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. 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]


  1. ^ a b 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. Archived from the original on 5 March 2016. 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.

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