Many seemingly complex features of the world and universe are built from repeating units that combine regularly to assemble astoundingly beautiful structures. From sea shells and spiral galaxies to cauliflower florets and the leaves on a tree, repeating patterns shape our universe.

This month’s project is a model of a truncated icosahedron, a planar combination of hexagons and pentagons. You might recognize this pattern as the shape from a soccer ball. This model was developed by George W. Hart.

While it looks complicated, this is a relatively simple model to construct and is a good place to start for beginners. This example is made from 20 3″ triangles cut from scrap cardboard. You can also use other types of paper, such as construction paper or poster board.

Materials needed:

• Ruler
• Scissors
• Pencil
• Compass
• White glue
• 9″ by 12″ of scrap cardboard

Cut out the triangles:

1. Use the pencil, ruler, and compass to draw a 3” equilateral triangle.
2. Cut it out.
3. Trace 20 copies of the triangle and cut them out.
4. On each triangle, cut a slit on each side, 1″ from the corner. Each slit should reach to the triangle’s midline. These slits will help each piece lock together when you assemble the model.

Tip: To make this process faster, cut a template using the 21st triangle you cut out earlier.

Once slits are cut on all three sides of all twenty triangles, you are ready for assembly.

Assemble the icosahedron:

1. Slide two triangles together, by their slits.
   
2. Add three more triangles to make a ring of five triangles.
   
3. Add another triangle to each of the free points on the ring.
   
   
4. Then, to create an alternating row, connect a new triangle to two of the triangles on the ring. This should form a pentagon-shaped space between the triangles.
   
   
5. Repeat step 4 with four more triangles, until the ring is complete. 
   
6. Fit the last five triangles across the ends to complete the polyhedra.
   

Tip: If you are having difficulty with pieces popping out while you are working dab a little white glue on the seams as you go.

Other ideas:

Try making paper sculptures in different sizes. The larger you go the more rigid your source material needs to be. Or go smaller to  make some lovely,  delicate models using decorative papers of all kinds.

If this type of project appeals to you, try the versatile and far more durable Space Chips available in many sizes and styles.