I designed this unit with Kazuyo Inoue, while at Queen's University, in Spring 1997.
It can be used to make various polyhedra with triangular faces,
such as the octahedron to the right, or the tetrahedra to the left, and
many more, shown below.
There are two versions, one from A4 paper (which will also work from other
size rectangles), and the other from square paper.
Click on any photo on this page to see a larger version.
Instructions for folding from a rectangle:
1. start with A4 paper, or other rectangular paper.
2. fold in half both ways and open out.
3. fold one short edge to the middle, make a crease on the lower part
of the fold, and open out.
4. Make a fold starting at the middle of the top, and made so that the
top right corner touches the crease mark shown. To help get the crease starting in the right place, put your finger at the top
mid point while bringing over the right corner.
5. Open out so it looks like this:
6. Fold the left half of the top edge to meet the diagonal fold on the right
of the paper:
7. open out:
8. Note the shaded hoizontal and diagonal creases:
9. Bring up the diagonal crease indicated in the last picture so that
it lies along the horizontal crease also shaded in the last picture:
10. Open out:
11. Repeat on the other side:
12. Open out:
13. Fold over the corners as shown:
14. Fold the short diagonal edges to meet the diagonal creases as shown:
15. Fold in along the diagonal creases as shown:
16. Turn over:
17. Fold down the corners that stick up over the edges:
18. Fold along the creases shown:
19. Turn over. This is the final unit from the front:
20. This is a photo of the final unit. Click on the image for a larger view.
You also need to be able to fold the mirror image version, which is the same to step 12, but then proceeds like this:
1. Take 5 units of each parity. Here 5 are shades of green and blue, and
the other 5 are shades of red and pink.
2. Take five of the same parity and fit them together like this:
3. Now join the first to the last. Now the model can not lie flat, and
it may help to use some paper clips to keep the pieces in place.
4. now the red/pink pieces go in place around the green/blue pieces. Here
is the first pink piece in place:
5. To put the red piece in position, first fold it over like this:
6. And slide it into place like this:
7. Then tuck the point into the next blue/green unit:
8. Now take the next pink/red unit:
9. Slide it into place like this:
10. And tuck in the pink point:
11. Next red/pink unit sliding into place:
12. And the point tucked in:
13. Final pink/red unit slides into place:
14. And its point tucks in.
15. Turn over the model:
16. Tuck in a loose pink corner into the next pink/red unit's spare pocket:
17. Then that units point is tucked into the next pocket:
18. And the next point into the next pocket:
19. And the next point into the next pocket:
20. And the final point is tucked into position to complete the model:
And here is the final icosahedra from another view. This
icosahedron is made from sheets of A4 paper. There is also a
picture of an icosahedron made from the units made from squares in the
set of pictures below.
This icosahedra is not very strong when made from paper.
But made from sheets of A4 card, with a little glue perhaps, to hold
some of the points in place, it is quite a strong model. Or, as an
alternative to glue, instead of having the points stick into the
upper opening, bend them downwards into the pocket with opening in
the same place, but facing the other direction.
Some more shapes you can make with this unit (click on image for a bigger
Tetrahedra do not tessellate; but if you put 20 together, you get
quite close to an icosahedron shape.
I've designed an icosahedron shaped box
to hold them. When I get time I'll add some instructions for how
to fold it. Here are a few images from a few different directions for
Icosahedral box (click on image for a bigger
This page transfered to http://make-origami.com/HelenaVerrill/home.php in May, 2015.