How to Construct Geometrical Solids, Icosahedron

The icosahedron is one of 5 platonic solids (the cube, tetrahedron, octahedron and dodecahedron being the other 4) and it has 20 faces of equilateral triangles. In geometry, the icosahedron is called the "dual" of the dodecahedron because each vertex of the icosahedron corresponds to a face of the dodecahedron, and vise versa.

With stiff paper, adhesive, and scissors, you can construct your own solid figure per the instructions below. You can use the icosahedron as a 20-sided die, or as a decoration.

Instructions

1. First, understand the basic shape of an icosahedron. In this solid shape, each vertex is where 5 equilateral triangles meet at a common point.

2. 

   To begin, cut out the figure shown. This pattern has ten triangular faces and represents 1/2 of the finished shape.

3. Laying the figure flat on the table, fold all the edges upward with "valley" creases, so the the figure curls into itself. Glue the light blue tab onto the adjacent triangle as shown. Leave the dark blue tabs; they will be glued in the last step.

4. 

   Repeat Steps 2 and 3 for the next figure, which is the mirror image of the first. Always fold upward. Now you have two halves of the solid figure.

   Notice that when you put the two shells together, the 10 dark blue tabs will interlock with the 10 triangles.

5. 

   Fit the blue tabs on one shell underneath the triangles on the other shell. Make sure that you have 5 triangles meeting at every point. When the glue dries, you will have a completed icosahedron. You can use gold and silver foil paper to make a mirror ball, or use the pattern to construct a geometric pinata.

6. 

   You can also use this solid geometric shape to make a 20-sided die.