An investigation of platonic solids and molecular symmetry with Clifford algebra

ABSTRACT PhD Thesis AN INVESTIGATION OF PLATONIC SOLIDS AND MOLECULAR SYMMETRY WITH CLIFFORD ALGEBRA ABİDÎN KILIÇ Anadolu University Graduate School of Natural and Applied Sciences Physics Program Supervisor: Prof. Dr. Kudret ÖZDAŞ 2004, 103 pages In this thesis, after the general definition of the Clifford algebra, the geometrical properties of Clifford algebra in different dimensions are investigated, it is also applied to the symmetry operations, as well. Golden ratio and the rotational axis and planes of reflection are defined belonging to the Platonic solids. Symmetry groups of Platonic solids are established. The symmetry operations defining the Clifford algebra are applied to the Platonic solids. Advantageous and compact representations of symmetry operations with Clifford algebra are obtained. Keywords: Clifford algebra, Platonic solids, Tetrahedron, Cube, Octahedron, Ikosahedron, Dodecahedron, Symmetry operations, Group theory.