Contents
-
Imperfect Congruence
- A mathematical note
- About the author
- Part 1: Kepler and the regular polygon tilings
- Part 2: Rhomb/rhombus/rhombic tilings
-
Part 3: A universal tiler
- Fans and other rhombic structures
- Regular polygon decomposition
- Regular polygon decomposition (odd)
- Worms and zonagons
- Decomposition algorithm
- Decomposition mathematics
- Variations on the universal tiler
- The regular polygon extension theorem
- The triangle extension theorem
- The rule of two
- The vertex figure extension conjecture
- Vertex figure extension examples
- More vertex figure extension examples
- Part 4: Five-fold symmetry
- Conclusion
- Tiling Gallery
- Appendix: Bridges conference
- Appendix: Proof of the Gap Theorem
- Appendix: Tiling source code
Jeweled crown - a 4.5.20 thin tiling
The details of the construction of this tiling are in Constructing a thin 4.5.20 tiling. The tiling definition is below. The coloured tiling image appears chaotic but as you can see it the black and white version and in the two chapters on constructing the tiling and on some interesting features of the thin patch, it has a striking mixture of chaos and order.
A part of this tiling is used as the header image for this site.
Translational unit
Legend
Skeleton tiling
Tiling (black and white)
Translational unit (black and white)
