One of the most intriguing concepts that caught the imagination of Plato around the time of 350 B.C. was the existence and uniqueness of the five regular solids, which are now known as the five "Platonic solids". It is not certain who first discovered these regular solids first, but many believe that it was spoke of as early as the Pythagoreans. However, sources including Euclid indicate that Theaetetus, a friend of Plato's, was the first to write the first complete account of these five shapes. Plato's theory ultimately constructs the basis for what is to be Book XIII of Euclid's Elements. Plato, in any case, was extremely impressed by these definitively regular solids, and later on in life was intrigued to write his theory of everything in relation to these five polyhedrons. (Devlin 115)
             The most intriguing aspect of these shapes to Plato at the time was that these were the only shapes that constituted perfect symmetry within a non-planar set of points. The names of these shapes are the hexahedron (cube), tetrahedron, octahedron, icosahedron and the dodecahedron. It is very clear that each of the sides of these polyhedrons must not only be a regular polygon, but must be equal to every other polygon within the shape. The first and most simple of these shapes is the tetrahedron. Having four faces, the tetrahedron is composed of four equilateral triangles. This shape constitutes that if three equilateral triangles meet at every vertex within a polyhedron, it creates a tetrahedron.
             If we take the same idea, using equilateral triangles, and change the number of triangles that converge from three to four, we end up with an octahedron. The octahedron resembles two pyramids bottom to bottom, which creates eight equilateral triangles exposing a perfectly symmetrical shape.
             The next of the polyhedrons is the icosahedron. Again, if we take the same idea involving a
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