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

The group cmm has reflections in two perpendicular directions, and a rotation of order two (180°) whose centre is not on a reflection axis. It also has two rotations whose centres are on a reflection axis.

Orbifold signature: 2*22
Coxeter notation (rhombic): [∞,2+,∞]
Coxeter notation (square): [(4,4,2+)]
Lattice: rhombic
Point group: D2

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