Planar P3 Penrose Tiling

thingiverse

This is a planar P3 Penrose tiling designed in OpenScad for MATH 493: Math Through 3D Printing at George Mason University in Fairfax, VA. The STL files for the patch of tiling and for the individual tiles are included with this submission. The tiles are made by extruding and intruding circular arcs to visually show the matching rules for creating Penrose tilings that follow a specific pattern. A photo of a section of a P3 tiling made in OpenScad is also included, along with a hand-drawn image showing the inflation of the tiles. Since this tiling follows both the inflation/deflation rules and the matching rules, we know that this is a Penrose tiling that can continue on infinitely. The tiling pattern used in this design is a common P3 tiling pattern known for its unique properties. The planar P3 tiling was discovered by Roger Penrose and Robert Ammann separately in the 1970s. Print Settings: * Printer Brand: MakerBot * Printer Model: MakerBot Replicator (5th Generation) * Rafts: Not Required * Supports: None How I Designed This: The tiles were designed using a combination of mathematical calculations and computer-aided design software. The necessary side lengths to fulfill the angle requirements of a Penrose rhomb were calculated, then circular arcs with the necessary radii were overlayed to accurately display the matching rules for creating Penrose tilings.