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Imperfect Congruence

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Home » Imperfect Congruence » Part 2: Rhomb/rhombus/rhombic tilings » Tilings from Robert Fathauer » Compass - a 4.5.20 tiling

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)

‹ Rockets - a 3.10.15 tiling up Broken roses - three 5.5.10 tilings ›

Content

  • A mathematical note
  • About the author
  • Part 1: Kepler and the regular polygon tilings
  • Part 2: Rhomb/rhombus/rhombic tilings
    • Pentagon tilings
    • Rhomb tiling and extension
    • Gears - a 5.5.10 tiling
    • Globe - a 4.5.20 tiling
    • Milkmaid - a 3.8.24 tiling
    • Warrior - a 3.9.18 tiling
    • Nutshell - a 3.10.15 tiling
    • Mirror - a 3.7.42 tiling
    • Tilings from Robert Fathauer
      • Shield - a 3.7.42 tiling
      • Dancer - a 3.8.24 tiling
      • Starburst - a 3.8.24 tiling
      • Art - a 3.9.18 tiling
      • Waves - a 3.9.18 tiling
      • Fighters - a 3.10.15 tiling
      • Rockets - a 3.10.15 tiling
      • Compass - a 4.5.20 tiling
      • Broken roses - three 5.5.10 tilings
  • Part 3: A universal tiler
  • Part 4: Five-fold symmetry
  • Conclusion
  • Tiling Gallery
  • Appendix: Bridges conference
  • Appendix: Proof of the Gap Theorem
  • Appendix: Tiling source code
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