This 8 sided shape made of equilateral triangles is very pleasing to look at and has some interesting qualities.

some Octoheadrons

Gather some materials

  1. Paper
  2. Pencil
  3. Calculator
  4. Ruler
  5. Eraser
  6. Scissors
  7. Tape

Calculate the height of your equilateral triangle (rows)

There are a few ways you could do this but the best is using Pythagoras. I decided to use a triangle that has 4cm sides.

Pythagoras

So with a height of 3.46, we will want 3 rows, so we now have 3 measurements to make, 3.46, 3.46 x 2, and 3.46 x 3 -> 3.46, 6.93, 10.39 cm.

Mark the rows on the page

Using a ruler start from the top of the page and mark 3 points along the left edge of the page. Do the same on the right edge then draw lines between them. Optional - leave a margin of 1 cm along the top and measure your lines from that.

rows

Mark a left margin

We could use the edge of the page for an origin but leaving some space will allow for flaps. Make a vertical line 1 cm from the left edge of the page.

Mark the corners along your rows

If you used a different edge length you will have to scale your distances, but using the side of length 4 cm you can use the following distances from the left margin

Row cm from left edge
1st row 8, 12
2nd row 2, 6, 10
3rd row 0, 4, 8, 12
4th row 6

rows with corners

The first row is the top of the page, or if you decided to make a top margin and mark your rows from that.

Mark the triangles

You can do this with 3 lines sloped up and 3 lines down. The result will have 2 triangles in the top row 5 in the middle row and one in the bottom row.

triangles

Cut out leaving room for flaps

Every outside edge should have a flap so we will NOT be cutting on the lines. So cut about 4 mm from the edges.

cut out with padding

You can see now that I should have used a top margin because the 2nd triangle in the top row will not have a flap … next time!

Trim flaps

The flaps will run into each other if you do not trim them.

trim flaps

Crease folds

Every triangle edge needs a crease. Fold them in where possible but you may need to fold them out the first time and then reverse the fold. Start your folds in the middle and then move to the edges.

crease folds

Tape it together

I do not put tape on the flaps, they are simply there to push out on the edges. I put tape on the outside doing one edge at a time tucking the flaps inside. You may decide to trim the flaps more if the corners are not coming together.

Voila, C’est un Octoheadron!

voila