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Real basis functions of polyhedral groups
- Publication Year :
- 2016
-
Abstract
- The basis of the identity representation of a polyhedral group is able to describe functions with symmetries of a platonic solid, i.e., 3-D objects which geometrically obey the cubic symmetries. However, to describe the dynamic of assembles of heterogeneous 3-D structures, a situation that each object lacks the symmetries but obeys the symmetries on a level of statistics, the basis of all representations of a group is required. While those 3-D objects are often transformed to real functions on $L_2$ space, it is desirable to generate a complete basis on real space. This paper deduces the existence of a basis on real space for each polyhedral group, and introduces a novel approach to explicitly compute these real basis functions, of which properties are further explored.
- Subjects :
- Mathematics - Group Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1611.06472
- Document Type :
- Working Paper