README.md

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Tiling of the Plane with Regular Polygons

This repository features a unique tiling of the plane with regular polygons, showcasing all vertex types except for the 4-8-8 configuration. Special thanks to Samy Meziane for providing this remarkable example.

Visualizing the Tiling and Its Duals

Original Tiling

Below is the original tiling of the plane with regular polygons:

Dual Tiling

The dual tiling of the original configuration:

Bidual Tiling

The bidual tiling (dual of the dual):

Tridual Tiling

The tridual tiling (third dual):

Quadrial Tiling

The quadrial tiling (fourth dual):

Higher-Order Dual Tilings

The process of deriving duals can be repeated indefinitely. Below are the visualizations up to the 15th-order dual:

Fifth Dual Tiling

Sixth Dual Tiling

Seventh Dual Tiling

Eighth Dual Tiling

Ninth Dual Tiling

Tenth Dual Tiling

Eleventh Dual Tiling

Twelfth Dual Tiling

Thirteenth Dual Tiling

Fourteenth Dual Tiling

Fifteenth Dual Tiling

Acknowledgments

Special thanks to Samy Meziane for his contribution to this fascinating exploration of planar tilings.