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
Broken roses - three 5.5.10 tilings
These three tilings, sent to me by Robert Fathauer, all have small translational units.
None of them allow a full rose of pentagons around a central decagon, so I have called them broken rose tilings.
Broken rose 1 and 2 are both nutshell tilings - the decagons and pentagons form “nutshells” entirely enclosing the rhombs.
Broken rose 1
Broken rose 2
Broken rose 3
