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
Dancer - a 3.8.24 tiling
The Dancer tiling is constructed in part from an irregular polygon that occurs twice (once rotated by 180°) in the transla-tional unit. It is remarkably similar to the shield jewel in the 3.7.42 Shield tiling.
It is constructed from a nutshell that contains three 24-gons alternating with three octagons:
Tiling
Translational Unit
Legend
Skeleton tiling
Tiling (Black and white)
Translational Unit (Black and white)
