Wallpaper group p2

thingiverse

This is part of a comprehensive set of 17 items showcasing all wallpaper groups, designed to facilitate learning about symmetry. "A wallpaper group, also known as a plane symmetry group or plane crystallographic group, is a mathematical classification of two-dimensional repetitive patterns based on their symmetries. Such patterns are commonly found in architecture and decorative art, particularly in textiles and tiles as well as wallpaper." https://en.wikipedia.org/wiki/Wallpaper_group This item includes customizable tiles for creating patterns with the correct symmetry. The tiles feature an embossed swirl pattern that aids in observing rotation, translation, reflections, and glide planes. Straight edges clearly indicate mirror symmetry. Files: p2-cutout.stl - the asymmetric unit. p2-cutout-swirl.stl - optional insert for the asymmetric unit. The figure illustrates the symmetry elements for this group. OpenSCAD files are available upon request. Wallpaper group p2 consists of two tiles per unit cell. The group p2 contains four rotation centers of order two (180°), but no reflections or glide reflections. Orbifold signature: 2222 Coxeter notation (rectangular): [∞,2,∞]+ Lattice: oblique Point group: C2