The Platonic Solids
نویسنده
چکیده
The tetrahedron, the cube, the octahedron, the dodecahedron, and the icosahedron. From a first glance, one immediately notices that the Platonic Solids exhibit remarkable symmetry. They are the only convex polyhedra for which the same same regular polygon is used for each face, and the same number of faces meet at each vertex. Their symmetries are aesthetically pleasing, like those of stones cut by a jeweler. We can further enhance our appreciation of these solids by examining them under the lenses of group theory – the mathematical study of symmetry. This article will discuss the group symmetries of the Platonic solids using a variety of concepts, including rotations, reflections, permutations, matrix groups, duality, homomorphisms, and representations.
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