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
Part 2: Rhomb/rhombus/rhombic tilings
Warrior - a 3.9.18 tiling
3.9.18 jewel.
The translational unit contains three identical patches and three 18-gons. The patches are irregular convex polygons with two 9-rhomb and two 18-rhomb shaped chunks taken out of them. The illustration shows this “jewel” with the rhombs added back.
In the full tiling, each rose with alternating triangle and nonagon petals is surrounded by six non-rose 18-gons.
Tiling
Translational Unit
Legend
Skeleton tiling
