Wallpaper group cm

thingiverse

This is part of a comprehensive set of 17 things representing all wallpaper groups, designed for mastering symmetry. "A wallpaper group (or plane symmetry group or plane crystallographic group) classifies a two-dimensional repetitive pattern mathematically, based on the symmetries within it. 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 have an embossed swirl pattern that aids observation of rotation, translation, reflections, and glide planes. Straight edges indicate mirror symmetry. Files: cm-cutout.stl - the asymmetric unit. cm-cutout-swirl.stl - optional insert for the asymmetric unit. cm-cutout-m.stl - mirror image asymmetric unit. cm-cutout-swirl-m.stl - optional insert for the mirror image asymmetric unit. The figure displays the symmetry elements for this group. OpenSCAD files are available upon request. Wallpaper group cm has four tiles per unit cell. Orbifold signature: *× Coxeter notation: [∞+,2+,∞] or [∞,2+,∞+] Lattice: rhombic Point group: D1 The group cm contains no rotations. It has reflection axes, all parallel. There is at least one glide reflection whose axis is not a reflection axis; it is halfway between two adjacent parallel reflection axes.