Gailiunas's Spiral Tilings

Explore a series of 52 spirals made from intersecting regular polygons with up to 36 vertices.



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Paul Gailiunas [1] found a method that can produce spirals with three or more arms. This Demonstration shows 52 spirals made from intersecting -gons up to with all possible numbers of arms from 3 to 18. The basic polygonal tiles can be considered as bent wedges with three boundaries made of equal edges: a base of 1 segment, a convex side using segments and a concave side using segments. For fewer arms, several spirals with the same number of arms originating from different -gons are given.
These monohedral spiral tilings are nonperiodic, have rotational symmetry and tile the plane.
"arms, , ": select one of the 52 spirals with the given number of arms, made from a specific -gon, using segments at the convex side.
"levels": controls the length of the arms.
"edges": use this checkbox for enhancing the boundaries of the polygons.
"color count": set the number of cyclic colors selected from the color palette popup menu. Selecting "arms" provides different colors for each arm.
[1] P. Gailiunas, "Spiral Tilings," in Bridges: Mathematical Connections in Art, Music, and Science, Winfield, KS: Bridges Conference, 2000 pp. 133–140. archive.bridgesmathart.org/2000/bridges2000-133.pdf.
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