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
Milkmaid - a 3.8.24 tiling
An octagon Easter egg and a larger convex "jewel".
The translational unit also contain two copies of another convex irregular polygon jewel, best seen in the alternative colouring below. One copy is a rotated version of the other.
Every 24-gon is the centre of a rose with alternating triangle and octagon petals.
The tiling requires three regular polygon and three rhomb prototiles to complete. The rhombs are the 8-rhomb, the 12-rhomb and the 24-rhomb.
It would be interesting to know if it is possible to construct a rhomb and regular polygon tiling with both 3.8.24 and 4.8.8 vertex types.
Tiling
Translational Unit
Legend
Skeleton tiling
Tiling (Alternative colouring)
Translational Unit (Alternative colouring)
Tiling (Black and white)
Translational Unit (Black and white)
