Wallpaper group p4

thingiverse

This is part of a set of 17 things representing all wallpaper groups, designed for learning about symmetry. "A plane symmetry group or plane crystallographic group, also known as a wallpaper 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, tiles, and 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: p4-cutout.stl - the asymmetric unit. p4-cutout-swirl.stl - optional insert for the asymmetric unit. The figure shows the symmetry elements for this group. OpenSCAD files are available on request. Wallpaper group p4m has four tiles per unit cell. The group p4 has two rotation centres of order four (90°), and one rotation centre of order two (180°). It has no reflections or glide reflections. Orbifold signature: 442 Coxeter notation: [4,4]+ Lattice: square Point group: C4