Tetrahedron Wall Art

When I left my first teaching school (the one I’m back working at again now) I decided to make a piece of art as a leaving gift for my colleagues in the maths team. I’d seen an image on Pinterest of a mural made from different coloured paper tetrahedra, and wanted to try it for myself. However, being a maths teacher, I was intrigued by the possibilities of tessellating smaller tetrahedra within the gaps left by bigger tetrahedra....

Now I know that A-sized paper has some pretty cool properties, so, using the photocopier I reduced an A4 tetrahedron net down through the various A-sizes - and, yes, I made some lovely discoveries (which made perfect sense once I started thinking about it)!

Each iteration of A-sized paper decreases in area by half, (so the side lengths decrease by a factor of 1/(sqrt2)): A5 is half the area of A4, A6 half the area of A5, and so on. So the base of an A6 tetrahedron is a quarter the area of an A4 base, meaning that four A6 tetrahedron bases can be packaged in the gap left by an A4 tetrahedron. I played around and found some other combinations (see some examples below).

---

I printed and cut out all my nets, assembled my different sized tetrahedra (step-by-step instructions to follow below) and played around with lots of different arrangements. When finally happy, I stuck them down onto a ready-made canvas.

A week ago my ex-colleague Ali got in touch because she wanted to try the activity with her class. I talked her through the instructions and her students went on to produce the wonderful artwork below :)

Here are the step-by-step instructions if you would like to try this activity with your students.

Resources:

• Tetrahedron net with tabs - SEN Teacher does one here.
• Different coloured card
• Scissors
  
• Ruler
  
• Ballpoint pen for scoring the card
  
• Glue
• Backing paper or ready-made canvases

Instructions:

1. Print out your 'master' tetrahedron net onto A4, then use the photocopier to reduce this to produce A5, A6 and A7 templates (and A8 if you're feeling brave). I photocopied several smaller templates onto one page, to reduce the amount of card needed.
2. Now photocopy your different sized nets onto stiff coloured paper or card (I used 160 gsm card).
3. Cut out the nets (being careful not to cut off the tabs!).
4. Now 'score' the fold lines by running a ballpoint pen firmly along each line using a ruler. This will ensure the nets fold up easily and give a perfect crisp edge.
   
5. Next assemble the tetrahedra by gluing the tabs - a tacky but quick-drying glue is best for this.
6. Finally play around with a design built from different-sized, different-coloured tetrahedra, and when happy, stick them onto good quality backing paper (don't use sugar paper as it will soon fade and look tatty), or on to a ready-made canvas (The Works or The Range do large packs quite cheaply).
7. Step back and enjoy your handiwork!