Make a straight line of 10 triangles.
When everything is dry, you can begin final assembly. First, take the straight line and bend it around into a ring. Then glue the two ends together.
Put one of the groups of five triangles on top, so it matches the tabs on the ring. Glue it down and wait for the glue to dry.
Finally, turn the ring over and stick the final group of five triangles on the other side of the ring. When the glue is dry, you’ll have a cool decoration!
What’s happening?
How do you make something round out of something flat? The secret is in the corners.
If you take a point on a flat piece of paper and divide it up into angles, they will always add together to make 360 degrees. If you look at the angles on this bauble, that’s not always the case.
At each vertex (3D corner), five equilateral triangles meet. Each of these is a 60 degree angle, so they add up to 300 degrees. This is why the triangles can’t lie flat – there’s not enough angle at this point.
This shape is an icosahedron, one of the 3D shapes known as platonic solids. They are all made up of regular flat shapes, and the angles at each vertex always add up to less than 360 degrees.
The five platonic solids are the triangular pyramid (three triangles meet at each vertex), the cube (three squares meet), the octahedron (four triangles meet), the dodecahedron (three pentagons meet) and the icosahedron (five triangles meet).
To make equilateral triangles lie flat, you need six of them to meet at each point. Then the angles add up to 360 degrees, and you’ll have what is known as a tessellation.
If you try putting seven triangles together, you’ll start making a completely different shape, known as a hyperbolic surface. They are pretty wacky – if you have a lot of time, try making one!
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