Faraad Armwood, NDSU

Math Club, May 08, 2015.

Title:  Order of Symmetry Groups for Regular Polygons and Platonic Solids

Abstract:  In the case of regular polygons, computing the order of the corresponding symmetry group by consequence of planar isometries is rather simple (which is where we will begin). For platonic solids, visualizing the transformation under each symmetry via rotational axis is a rather computationally hazardous way of going about things. However, It turns out that there is a very beautiful relationship between the orbit and stabilizer afforded by the group action (symmetries) which will make our lives much easier. This relationship will be the primary focus of this talk. 

Prerequisites: Group, subgroup, index, orbit, stabilizer, and group action which I will define and give examples for in the first  20-25 minutes of the talk.