Symmetry Cubes

One can use a simply decorated cube to construct examples of frieze patterns and some of the wallpaper patterns. See my paper Symmetry Patterns from Multiple Identically Patterned Cubes from the 2019 Bridges Conference.

strips for cube
The six strips shown above can be assembled into a cube shown below.
assembled cubes
Two views of an assembled cube from the strips shown above. These were built using heavy paper. The cube will hold together with friction but you can also use tape or glue to help keep the cube together.

Download a printable page, CubeStrips.pdf, that you can use to make a symmetry cube. They can be assembled in a process similar to the process described in the video How to make paper cube easy way.