Wallpaper group pgg

thingiverse

This is part of a comprehensive set of 17 items showcasing all wallpaper groups, designed to facilitate 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 in 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 correct symmetry. The tiles have an embossed swirl pattern that is helpful for observing rotation translation reflections and glide planes. Straight edges indicate mirror symmetry. Files: pgg-cutout.stl - The asymmetric unit. pgg-cutout-swirl.stl - Optional insert for the asymmetric unit. pgg-cutout-m.stl - Mirror image asymmetric unit. pgg-cutout-swirl-m.stl - Optional insert for the mirror image asymmetric unit. The figure shows the symmetry elements for this group. OpenSCAD files are available upon request. Wallpaper group pgg has four tiles per unit cell. The group pgg contains two rotation centres of order two 180° and glide reflections in two perpendicular directions. The centres of rotation are not located on the glide reflection axes. There are no reflections. Orbifold signature: 22× Coxeter notation (rectangular): [((∞,2)+,(∞,2)+)] Coxeter notation (square): [4+,4+] Lattice: rectangular Point group: D2