Wallpaper group p4g

thingiverse

This is part of a set of 17 things representing all wallpaper groups, designed for studying 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 in them. Such patterns appear 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 right symmetry. The tiles have an embossed swirl pattern that helps observe rotation, translation, reflections, and glide planes. Straight edges indicate mirror symmetry. Files: p4g-cutout.stl - the asymmetric unit. p4g-cutout-swirl.stl - optional insert for the asymmetric unit. p4g-cutout-m.stl - mirror image asymmetric unit. p4g-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 p4g has eight tiles per unit cell. The group p4g has two centers of rotation of order four (90 degrees), which are each other's mirror image, but it has reflections in only two directions, which are perpendicular. There are rotations of order two (180 degrees) whose centers are located at the intersections of reflection axes. It has glide reflections axes parallel to the reflection axes, in between them, and also at an angle of 45 degrees with these. Orbifold signature: 4*2 Coxeter notation: [4+,4] Lattice: square Point group: D4