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
Compass - a 4.5.20 tiling
This tiling, sent to me by Robert Fathauer, is composed of two simple nutshells of alternating icosagons (20-gons) and pentagons. One of these is the simplest possible nutshell - its interior “nut” is a single square!
The four narrow 20-rhombs at the centre of the larger nutshell remind me of the points of a compass.
Tiling
Translational Unit
Legend
Skeleton tiling
Tiling (Black and white)
Translational Unit (Black and white)
