News: 7 Templates for Slide-Together Geometric Paper Constructions

The "slide-together" paper construction method is a fun and satisfying way to build 3D geometric objects. It only requires paper, scissors or an exacto knife, and some patience.

In Tuesday's post, we explored the slide-together method, using ordinary playing cards to build the platonic solids. In today's post, we are going to extend this method by making polyhedral objects using regular polygons cut out of card stock. George Hart has both designed and provided brief instructions on constructing six different fascinating geometric objects in this manner.

Last night I made two of them out of brightly colored cardstock:

To make these paper sculptures, you can use the template links I've provided below in pdf format. You can print them to whatever scaling you like, as long as you keep all of the polygons for each sculpture consistent. Once you've printed them out on cardstock, you must cut out the polygons and all of the slits.

• 12 Decagons Template

• 20 Triangles Template

• 12 Decagrams Template

• 20 Hexagons Template

• 12 Pentagons Template

• 12 Pentagrams Template

• 30 Squares Template

George Hart gives a basic idea of how to construct these on this page. However, it seems that he wants it to remain a little bit of a puzzle. In fact, he recommends using this construction process as a way to teach mathematical thinking and communication. So I'm not going to give step-by-step instructions on how to build these. I'll let you puzzle your way through it.

Here are my solutions, which I hope demonstrate some of the beauty of these objects.

Dodecahedral object made from 12 decagons:

Same dodecahedral object from an angle emphasizing the pentagons formed by the intersecting decagons:

Object made from 20 intersecting triangles that is based off the truncated icosahedron (soccer ball):

Same object, but from an angle emphasizing the 5 pointed stars (pentagrams) formed by the intersecting triangles:

Image showing the soccer ball-like interior of the object:

I hope you try making one or more of them. They really are fascinating objects to hold in your hand. If you do, post up pictures on the corkboard.