Wallpaper group p6

thingiverse

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: p6-cutout.stl - the asymmetric unit. p6-cutout-swirl.stl - optional insert for the asymmetric unit. The figure shows the symmetry elements for this group. openSCAD files are available upon request. Wallpaper group p6 has six tiles per unit cell. The group p6 has one rotation centre of order six (60°); two rotation centres of order three (120°), which are each other's images under a rotation of 60°; and three rotation centres of order two (180°) which are also each other's images under a rotation of 60°. It has no reflections or glide reflections. Orbifold signature: 632 Coxeter notation: [6,3]+ Lattice: hexagonal Point group: C6