The Infinite Pattern That Never Repeats (Kite and dart tiling)

A bit of theory:

Kite and dart tiling (P2) is a type of aperiodic tiling discovered by Roger Penrose. It uses two shapes — a kite and a dart — that fit together in a non-repeating pattern. Despite the lack of periodic repetition, the tiling shows fivefold symmetry and covers the plane without gaps or overlaps.

Dimensions & Compatibility:

• Tested on Prusa MK4S printer
• Recommended materials: PLA or PETG
• Includes ready-to-print G-codes
• The provided .stl model can be reduced to 1/3 of its size and still function perfectly.

Print settings:

• 2 perimetres
• 15% infill
• Print orientation as in the provided file
• Prints without supports, 0.15 mm layer height, 0.4 mm nozzle
• The concentric pattern on the bottom layer looks nice.

Assembly:

• Simple snap-fit solution

• This tiling pattern follows certain rules.
  • One rule is greatly simplified by the connectors I have created. The lines should be connected.
  • There must be no gaps or overlaps during assembly. That should be easy to follow.

• And yes, it moves like fabric after assembly, but it also has its own rules of movement, depending on which part of the pattern you assemble.

If you have any ideas or feedback about the model, please let me know.