People have been fascinated by symmetrical shapes for thousands of years. Plato, the famous Greek philosopher, played around with simple 2D shapes such as triangles, squares and pentagons (5 sides) and used them to construct 3D objects.
By just taking triangles for example we can make some wonderfully symmetrical shapes. For example if we take 4 triangles we get a tetrahedron and 20 triangles gives us the icosahedron (see picture of the crystals). In all these wonderfully symmetrical objects all the faces are the same as each other, all the corners are identical to each other and all the edges are the same as every other edge. These are just 2 of the set of 5 famous Platonic solids that have these unusual symmetrical properties.
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The platonic solids (cut-quartz) from left to right: a tetrahedron, cube, octahedron, dodecahedron and the icosahedron. These objects are remarkably symmetrical and in each shape every face, edge and corner are identical with every other face, edge and corner.
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