The symmetry group of a 3-dimensional figure is the set of all distance preserving maps, or isometries, of JR3 which map the figure to itself, and with composition as the operation. As we will see, we can use Maple not just to determine the elements of a sym- metry group but to identify the group, once,we apply the appropriate group theory. By determining a symmetry group, we mean not just to determine its elements but to identify it, up to isomorphism, with a well-known group, such as a symmetric or alternating group. The five platonic solids are the tetrahedron, the cube, the octahedron, the dodecahedron, and the icosa- hedron. In this article we will determine the symmetry groups of the platonic solids by a combination of some elementary group theory and use of the computer algebra package Maple.
0 Comments
Leave a Reply. |