Patrick Morandi’s research is primarily in the area of abstract algebra, notably in the study of finite-dimensional division algebras. His interest in calculating the symmetry groups of the platonic solids developed while he was teaching a course in abstract algebra and trying to introduce the students to Maple.

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. The five platonic solids are the tetrahedron, the cube, the octahedron, the dodecahedron, and the icosahedron. 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. As we will see, we can use Maple not just to determine the elements of a symmetry group but to identify the group, once we apply the appropriate group theory.

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Address for Correspondence
Patrick J Morandi
Department of Mathematical Sciences
New Mexico State University
Las Cruces NM 88003, USA
Email: pmorandi@nmsu.edu