Wallpaper group p31m

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This is part of a comprehensive set of 17 designs representing all wallpaper groups, specifically created to facilitate learning about symmetry. "A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of two-dimensional repetitive patterns based on the symmetries they contain. Such patterns frequently appear in architecture and decorative art, particularly in textiles, tiles, and wallpaper." https://en.wikipedia.org/wiki/Wallpaper_group This design includes customizable tiles for creating patterns with precise 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: p31m-cutout.stl - the asymmetric unit. p31m-cutout-swirl.stl - optional insert for the asymmetric unit. p31m-cutout-m.stl - mirror image asymmetric unit. p31m-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 p6m has six tiles per unit cell. The group p31m possesses three distinct rotation centers of order three (120°), with two being each other's mirror image. It includes reflections in three distinct directions, as well as at least one rotation whose center does not lie on a reflection axis. Additionally, there are glide reflections in three distinct directions, located halfway between adjacent parallel reflection axes. Orbifold signature: 3*3 Coxeter notation: [6,3+] Lattice: hexagonal Point group: D3