By George Hart for the Museum of Mathematics


What could sound easier than to make a regular construction from four paper equilateral triangles? One possible construction is the regular tetrahedron, which is pretty easy. Here is a different construction from four equilateral triangles. Each triangle is linked with the other three, like two links of a chain.

Use this template, in which each triangle has a hole cut from it, with exactly half the edge length. You’ll need to cut through three of them to link them together. After you assemble them properly, you can tape the cut back together.

Cory Poole took this idea and miniaturized it, making a lovely pair of geometric earrings from paper painted with metallic paint.

Instructions for assembling the triangles are available here, along with other polygon assembly challenges.

See all of George Hart’s Math Monday columns

Gareth Branwyn

Gareth Branwyn

Gareth Branwyn is a freelance writer and the former Editorial Director of Maker Media. He is the author or editor of over a dozen books on technology, DIY, and geek culture. He is currently a contributor to Boing Boing, Wink Books, and Wink Fun. And he has a new best-of writing collection and “lazy person’s memoir,” called Borg Like Me.

  • Francesco Mancini
  • Cory Poole

    The origami and pencil ones in the comment are really cool.  I’m also commenting because I’m Cory (not Corey  :)  )  Poole.

    • Gareth Branwyn

      Sorry about that Corey… er… Cory. Fixed!

      • Cory Poole

        Hah!  It’s ok.  I’m used to it.

  • hurlebaus

    Print twice, than make the cut on each set on a different place, mount together and glue than!