Wallpaper group pmg

thingiverse

This set of 17 items showcases all wallpaper groups, designed to educate people 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 symmetries within the pattern. Such patterns frequently occur 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 helps observe rotation, translation, reflections, and glide planes. Straight edges indicate mirror symmetry. Files: pmg-cutout.stl - the asymmetric unit; pmg-cutout-swirl.stl - optional insert for the asymmetric unit; pmg-cutout-m.stl - mirror image asymmetric unit; pmg-cutout-swirl-m.stl - optional insert for the mirror image asymmetric unit. The figure illustrates symmetry elements for this group. OpenSCAD files are available upon request. Wallpaper group pmg has four tiles per unit cell. The group pmg features two rotation centers of order two (180°), and reflections in only one direction. It also includes glide reflections whose axes are perpendicular to the reflection axes. The centers of rotation all lie on glide reflection axes. Orbifold signature: 22*; Coxeter notation: [(∞,2)+,∞] or [∞,(2,∞)+]; Lattice: rectangular; Point group: D2