Wallpaper group p3m1

thingiverse

This is part of a comprehensive set of 17 unique designs representing all wallpaper groups, designed specifically for learning about symmetry. "A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries present within the pattern. Such patterns are frequently encountered in architecture and decorative art, especially in textiles and tiles as well as wallpaper." https://en.wikipedia.org/wiki/Wallpaper_group This set includes tiles designed for creating patterns with the appropriate symmetry. The tiles feature an embossed swirl pattern that aids in observing rotation, translation, reflections, and glide planes. Straight edges indicate mirror symmetry. Files: p3m1-cutout.stl - the asymmetric unit. p3m1-cutout-swirl.stl - optional insert for the asymmetric unit. p3m1-cutout-m.stl - mirror image asymmetric unit. p3m1-cutout-swirl-m.stl - optional insert for the mirror image asymmetric unit. The figure illustrates the symmetry elements for this group. OpenSCAD files are available upon request. Wallpaper group p3m1 comprises six tiles per unit cell. The group p3m1 has three distinct rotation centres of order three (120°). It boasts reflections in the three sides of an equilateral triangle. The centre of every rotation lies on a reflection axis. There are additional glide reflections in three separate directions, whose axes are positioned halfway between adjacent parallel reflection axes. Orbifold signature: *333 Coxeter notation: [(3,3,3)] or [3[3]] Lattice: hexagonal Point group: D3