Cubes, Challenges, and Classroom Breakthroughs
I have long desired to do a unit based on 3D Tessellations but knew it would be challenging as I had never come across a lesson on something like this. 2D Tessellations are certainly fun and not too difficult. My approach (HERE) throws out the grid so even elementary students can do them.
But I wanted to be able to do what I have seen M.C. Escher do on rare occasions, and I did make some discoveries along the way. Below are 3 examples by the master himself.
But I wanted to be able to do what I have seen M.C. Escher do on rare occasions, and I did make some discoveries along the way. Below are 3 examples by the master himself.
After 3 weeks of struggle with my Art 3 high school class, we discovered that cubes, assembled with tessellations by rotation, can likely be done by middle school students. If you double the squares on each face, it looks more impressive and can be done by most high school students.
Other forms are far more challenging. For example, a 20-sided figure, an icosahedron, is made up of triangles. 5 triangles make up a portion of the form’s face. 3 does not go into 20, nor 5 easily… so creating a tessellation for such a form becomes more challenging. You can tessellate perhaps 50% of the form, but then overlaps and additional spaces need to be justified, or turned into additional figures so no empty spaces exist… otherwise it’s no longer a tessellation.
Here is a video that shows you my struggle and process with non-cube forms. They are not impossible; they are just very challenging.
Other forms are far more challenging. For example, a 20-sided figure, an icosahedron, is made up of triangles. 5 triangles make up a portion of the form’s face. 3 does not go into 20, nor 5 easily… so creating a tessellation for such a form becomes more challenging. You can tessellate perhaps 50% of the form, but then overlaps and additional spaces need to be justified, or turned into additional figures so no empty spaces exist… otherwise it’s no longer a tessellation.
Here is a video that shows you my struggle and process with non-cube forms. They are not impossible; they are just very challenging.
Tessellations with forms other than a cube CAN be done, but I would leave those for your design students, advanced classes, or those who find cubes too simple. Below are some of my Art 3 results. Some were able to do it well, and a couple struggled and “cheated” with empty spaces.
THIS VIDEO is an interesting one from TikTok on tessellations.
We created stands for some forms with coat-hanger wire and epoxy clay. They display nicely, and were appreciated by the math department, and used as an example of my intercurricular approach to my administration.
But let’s get back to cubes, which I think most classes can handle. If you create tessellations by reflection with squares, they can become cubes more easily. The video below shows the process of creating tessellations in this method. (THIS is a playlist of other tessellation techniques)
But let’s get back to cubes, which I think most classes can handle. If you create tessellations by reflection with squares, they can become cubes more easily. The video below shows the process of creating tessellations in this method. (THIS is a playlist of other tessellation techniques)
Once students have made a pile of possible shapes, then it is time to test them before moving onto a form. If they cannot make it work on a sheet of copy paper, then it will not work on a cube. This will save you a ton of wasted time.
Once you confirm that the tessellation actually works, then you can move on to the cube form. I used high-quality watercolor paper, but you could put paper over a cardboard or foamcore cube for a rigid structure.
The following two videos will walk you through my process of making these impressive 3D cube tessellations. I think you could reasonably do this with grades 6 and up, perhaps as low as 4th grade if they were artistically inclined.
The following two videos will walk you through my process of making these impressive 3D cube tessellations. I think you could reasonably do this with grades 6 and up, perhaps as low as 4th grade if they were artistically inclined.
One final note on displaying these. For some reason, if a cube is set on its axis, as I have done here by “threading” a coat-hanger wire through it, it feels more visually impressive. Certainly, you can sit them flat on a shelf but they feel more static that way.
If you'd like some printable form templates you can copy for students, I created this resource HERE with lots of non-tessellation lessons. If you like this lesson and are interested in others, I have THIS book of K-12 art lessons, and THIS follow-up for over 100 combined unique, choice-based art experiences. To get early notifications of my lessons and others I am experimenting with, join my Facebook Group.
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