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.

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.

## 5 Comments

Have posted my version of the 30 squares on the corkboard. Not really neat enough - but nice build and pleasing result

I was wondering if anybody else has had any issues with the joins. To make sure that I copied the diagram exact, I placed a printed out copy on to a window and trace it there. I have noticed that some of the joints have meet as tidy as the displayed photos, which look pretty kewl :)

Another is to use origami units called sonobe, google and get the instruction, besides geometric shapes made from pentagons and hexagons but other structures connected with tubes etc.

I made a variation of the 20 triangle form, substituting hearts for the triangles. When assembling one has to make conscious decisions about the direction the hearts are going to face, but other than that it's straightforward.

http://extremecards.blogspot.com/2015/02/paper-globe-of-slide-together-hearts.html

How to make that model

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