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:
pmg-cutout.stl - the asymmetric unit.
pmg-cutout-swirl.stl - optional insert for the asymmetric unit.
pmg-cutout-m.stl - mirror image asymmetric unit.
pmg-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 pmg has four tiles per unit cell.

The group pmg has two rotation centres of order two (180°), and reflections in only one direction. It has glide reflections whose axes are perpendicular to the reflection axes. The centres of rotation all lie on glide reflection axes.

Orbifold signature: 22*
Coxeter notation: [(∞,2)+,∞] or [∞,(2,∞)+]
Lattice: rectangular
Point group: D2

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