Wallpaper group p3m1
Description
This is part of a set of 17 things representing all wallpaper groups, designed for 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 occur frequently in architecture and decorative art, especially in textiles and tiles as well as wallpaper." https://en.wikipedia.org/wiki/Wallpaper_group This thing includes tiles for creating patterns with the appropriate 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: p3m1-cutout.stl - the asymmetric unit. p3m1-cutout-swirl.stl - optional insert for the asymmetric unit. p3m1-cutout-m.stl - mirror image asymmetric unit. p3m1-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 p3m1 has six tiles per unit cell. The group p3m1 has three different rotation centres of order three (120°). It has reflections in the three sides of an equilateral triangle. The centre of every rotation lies on a reflection axis. There are additional glide reflections in three distinct directions, whose axes are located halfway between adjacent parallel reflection axes. Orbifold signature: *333 Coxeter notation: [(3,3,3)] or [3[3]] Lattice: hexagonal Point group: D3
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