Philosophers and mathematicians like Euclid (300BC) were once ridiculed for suggesting that all matter was, at a basic level, constructed from one of the five platonic solids. We now know this to be true.
Platonic solids, named after Plato, have at least 3 faces meeting at each vertex (maybe more). When you add up the internal angles that meet at a vertex, it must be less than 360 degrees (at 360° the shape would flatten out). All the shape's faces are all identical regular polygons. In a nutshell, it is impossible to have more than 5, because any other possibility would violate simple rules about the number of edges, corners and faces you can have together.
Here's an amazing example of an icosahedron in nature:
http://upload.wikimedia.org/wikipedia/commons/0/0e/Haeckel_Phaeodaria_1.jpg
More info:
http://www.mathsisfun.com/geometry/platonic-solids-why-five.html
Platonic solids, named after Plato, have at least 3 faces meeting at each vertex (maybe more). When you add up the internal angles that meet at a vertex, it must be less than 360 degrees (at 360° the shape would flatten out). All the shape's faces are all identical regular polygons. In a nutshell, it is impossible to have more than 5, because any other possibility would violate simple rules about the number of edges, corners and faces you can have together.
Here's an amazing example of an icosahedron in nature:
http://upload.wikimedia.org/wikipedia/commons/0/0e/Haeckel_Phaeodaria_1.jpg
More info:
http://www.mathsisfun.com/geometry/platonic-solids-why-five.html
