If you’ve ever wondered how to make a tetrahedron, this project is a satisfying way to learn it, because you’re not just folding one, you’re building something that holds soil, water, and a living plant. A tetrahedron is one of the five Platonic solids, the regular polyhedra where every face is an identical equilateral triangle and every edge meets in the same way. It’s also one of the simplest forms in mathematics to construct from a flat sheet, which makes it a lovely, hands-on maths activity (or math, if that’s the word you grew up with) whether you’re a student, a teacher, or just someone who likes turning rubbish into something useful.
In the video above, I make mine out of an upcycled Tetra Pak carton rather than paper, because the laminated layers inside are naturally water-resistant. That property, which normally just keeps your juice or milk fresh, means the finished build can actually hold a small amount of soil without falling apart. This isn’t origami, and there’s no folding trickery involved; it’s a construction method. You draw the net, score it, cut it, and glue it together. Below is the full step by step video companion guide, with a bit more detail on the art and geometry behind each stage.
What You’ll Need
This is a low-cost, mostly-recycled project. Gather:
- One empty Tetra Pak carton (juice or milk both work), washed and dried
- A compass
- A ruler
- A thin felt-tip pen
- Scissors
- A hot glue gun
- A hole punch (or the tip of your scissors)
- A bottle top or similar circle, for tracing
- String, cut into three equal pieces
- Acrylic pens or other decorations
- Soil and a small plant
A note on the hot glue gun: this project uses one, so please check with an adult before using it, and make sure you’re supervised if needed.
What Is a Tetrahedron?
Before we get into construction, it helps to understand what you’re building. In geometry, a tetrahedron is a type of polyhedron with four triangular faces, four vertices, and six edges. It’s sometimes described simply as a pyramid with a triangular base rather than a square one. When all four faces are equilateral, each side the same length, it’s called a regular tetrahedron, and this is the version we’re making here.
The word comes from Greek: “tetra” means four, and “hedron” refers to a face, so tetrahedron literally means “four faces.” It belongs to a small, famous family of forms called the Platonic solids, five regular polyhedra where every face, edge, and vertex is identical. The tetrahedron is the simplest of the five, and the only one with just four sides, which is part of why it’s such a popular starting point for anyone learning tetrahedral geometry or exploring how a flat net can fold into a 3D form.
Preparing the Carton
Start by flattening your Tetra Pak. Pull apart the folds at the top until the carton opens out, then cut off the top and bottom to remove the lid and base. Cut down one side seam so you’re left with one flat rectangular sheet of material. Give the inside a wipe with a damp cloth or some kitchen towel; most cartons need a quick clean after they’ve held liquid, and a dry, flat sheet is much easier to work with accurately.
Drawing the Net of a Tetrahedron
This is the step that actually turns your flat material into a tetrahedron, and it’s worth taking slowly. The net is the 2D pattern that folds up into your finished form, made of four joined triangles.
- Draw a straight horizontal line near the bottom of your rectangle, and a vertical line up the right-hand side. These give you a right angle to work from, and leave room around the edges for the gluing flaps you’ll add later.
- Set your compass so the distance between the point and the felt-tip pen is 10cm. This will be the length of every side of every triangle, so keeping it consistent is what makes the finished form regular rather than lopsided.
- Starting from the bottom right of your rectangle, mark a point 10cm along your horizontal line. This gives you the base of your first triangle.
- Put the compass point on each of those two bottom points in turn and draw an arc from each, using your fixed 10cm spread. Where the two arcs cross is the apex. Join the marks to complete your first equilateral triangle.
- For the second one, move your compass point to the bottom-left of the first triangle’s base and to its apex, and repeat the same two-arc approach to find the next point.
- The third is quicker: put the compass point on the apex of the last one you drew, and mark a new point 10cm along the line. Then, exactly as before, use the base point and the apex to draw two more arcs, and join them where they meet.
By the end of this, you should have a strip of four triangles in a row, alternating point-up and point-down; this zigzag is the classic net used to create a tetrahedron.
Adding Flaps and Cutting Out the Net
Once your triangles are drawn, add small gluing flaps to three of the outer sides. They don’t need to be elaborate; a set square makes it easy to keep them a consistent width and angle.
Score each fold line using the back of your scissors or a ruler’s edge, working on the inside of the carton. This first pass makes the actual folding far cleaner and more precise on a stiffer material. Then cut out the whole net, flaps included.
Making It a Plant Pot, Not Just a Shape
At this point you could simply fold the flaps and glue everything shut, and you’d have a display piece or a maths teaching aid. But we’re making a plant pot, so there are two extra steps before any gluing happens.
First, trace around a bottle top (or any small circle) in the centre of one face, and cut or punch this out. This becomes the opening you’ll add soil through. Then, using a hole punch or the tip of your scissors, make a small hole in each of the three corners of that same triangle. These are for the hanging string.
Cut three equal lengths of string, roughly a ruler’s length each, and thread one through each hole before you glue anything closed, making sure the longer end of each piece sits on the outside.
Decorating and Planting
Before or after assembly, this is where you can make the project your own. I used acrylic pens with a white base layer to even out the colour on the Tetra Pak, but sequins, paint, or anything else that will stick works just as well.
Once your build is glued, decorated, and strung, add soil and a small plant. Because the folded seams of a tetrahedron aren’t fully sealed, water will find its way through the edges over time, so this pot suits plants that prefer misting or slightly damp soil rather than standing water; think succulents, air plants, or anything you’d normally reach for a spray bottle to water.
Gluing the Tetrahedron Together
Now fold along your scored lines and glue the three flaps down with the hot glue gun, taking your time and being careful with the heat. Once assembled, gather the three loose ends of string above the shape and tie a knot roughly two-thirds of the way up, so the finished pot hangs level rather than tilting to one side.
Why This Works as a Maths Project, Too
Beyond being a fun weekend craft, this is a genuinely useful way to explore geometry hands-on. You’re measuring consistent lengths with a compass, watching a flat sheet fold into a geometric solid, and ending up with a real Platonic solid rather than just reading about one in a maths textbook. It works well as a school project on shapes, and it’s easy to repeat once you understand the method, whether that’s with card, foam board, or another recycled carton.
How to Make a Tetrahedron Challenge
If you make your own tetrahedron plant pot, I’d love to see how you decorate yours. Tag me in your version on social media, and I’ll share your crafty creation. Tag @mathsinpractice on Instagram, Facebook, or TikTok, and let me know what you decide to grow in it.