We easily recognize symmetry in two dimensions. Reflectional symmetry is the easiest, but with practice the other types of symmetry can be spotted.
It is understandable that, when it comes to recognizing patterns, we simplify the world into two dimensions - those patterns on a rug, on a floor, or a wall.
The world, and the buildings around us, however, exist in three dimensions.
How much harder, then, is it to pick out symmetry in those objects.
Over two thousand years ago the Greeks defined 5 basic three dimensional objects - the regular Platonic solids - the cube, tetrahedron, octahedron, dodecahedron, and icosahedron.
Studying these objects reveals intriguing mathematical relationships between the numbers of faces, edges and nodes. The Greeks, and others since, attributed other meanings to these objects, such as beauty, truth, purity, as well as the basic elements.
Curiously, although the circle was an established two-dimensional figure to the Greeks, the sphere was not included among the Platonic solids.
The complexities of considering the symmetries of these three dimensional objects are dramatically greater than their 2D versions.
[attachment=1]Platonic solids.jpg[/attachment][attachment=0]cube_symmetry.jpg[/attachment]