Triangular Faced Origami Polyhedra 

Folding a unit from a square Putting together two units Making a tetrahedron Making an octahedron Making an icosahedron Other examples Home 

Introduction 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. 

 
 

And then you can make lots and lots of them:

Images of tetrahedra and octahedra:

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.
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 now.