Wallpaper group pmm

thingiverse

This is part of a comprehensive set of 17 items representing all wallpaper groups, designed to aid in learning about symmetry. "A mathematical classification system for two-dimensional repetitive patterns, based on the symmetries present within them, is known as a wallpaper group. These patterns frequently appear in architecture and decorative art, especially in textiles and tiles as well as wallpaper." https://en.wikipedia.org/wiki/Wallpaper_group This item includes tiles 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: pmm-cutout.stl - the asymmetric unit. pmm-cutout-swirl.stl - optional insert for the asymmetric unit. pmm-cutout-m.stl - mirror image asymmetric unit. pmm-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 pmm consists of four tiles per unit cell. The group pmm features reflections in two perpendicular directions, and four rotation centres of order two (180°) located at the intersections of the reflection axes. Orbifold signature: *2222 Coxeter notation (rectangular): [∞,2,∞] or [∞]×[∞] Coxeter notation (square): [4,1+,4] or [1+,4,4,1+] Lattice: rectangular Point group: D2