Exploring the Group Representation Theory of the Full Symmetry of Regular Tetrahedron

TL;DR

This paper investigates the symmetry group of a regular tetrahedron, detailing its algebraic structure, subgroups, and related mathematical properties, and also explores the Sudoku magic group.

Contribution

It provides a comprehensive analysis of the full symmetry group of the regular tetrahedron, including representations, subgroups, and algebraic structures, which was not previously detailed.

Findings

Derived the representation matrix and multiplication table of the symmetry group

Classified all subgroups, conjugacy classes, and cosets of the group

Discussed the properties of the Sudoku magic group

Abstract

In this paper we study the rotation and spatial inversion symmetry of regular tetrahedron. We obtain the representation matrix, multiplication table,the order of all group elements, all possible combinations of generator elements, the proper subgroups,conjugate classes, invariation subgroups and the corresponding cosets, quotients and homomorphic correspondence. In the end we discuss Sudoku magic group.