II. Triangular Prototiles

Only edge-to-edge tilings are listed here. At this time, I'm aware of only one family of such tilings with triangular prototiles. There are an infinite number of distinct tilings in this family, the first four of which are shown here. The prototiles for this family can be derived by taking segments of regular polygons containing two adjacent edges of the particular polygon. Polygons with number of sides 4, 6, 8, 10, 12, ... all yield edge-to-edge tilings.

The tilings are classified as described in the Introduction. The figures available for each tiling are listed as links.

The following paper, downloadable as a pdf file, describes this family of tilings as well as the quadrilateral family labeled "B".
Self-similar Tilings Based on Prototiles Constructed from Segments of Regular Polygons, presented at the Bridges Conference (July 28-30, 2000, Southwestern College, Winfield, Kansas). (File size - 660K.)

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