Surfaces with given Automorphism Group

Frucht showed that, for any finite group $G$, there exists a cubic graph such that its automorphism group is isomorphic to $G$. For groups generated by two elements we simplify his construction to a graph with fewer nodes. In the general case, we address an oversight in Frucht's construction. We prove the existence of cycle double covers of the resulting graphs, leading to simplicial surfaces with given automorphism group. For almost all finite non-abelian simple groups we give alternative constructions based on graphic regular representations. In the general cases $C_n,D_n,A_5$ for $n\geq 4$, we provide alternative constructions of simplicial spheres. Furthermore, we embed these surfaces into the Euclidean 3-Space with equilateral triangles such that the automorphism group of the surface and the symmetry group of the corresponding polyhedron in $\mathrm{O}(3)$ are isomorphic

EMMS: Increasing Hope and Transforming Lives Through Improved Access to Electrical Power

Developing countries often face a challenge involving energy conservation. Energy Monitoring and Management Systems (EMMS) was tasked to make an energy meter in order to provide a practical way of controlling energy consumption and create a tool for teaching energy conservation. This meter should be able to measure energy usage over a period of time and prevent further energy usage after a specified amount has been consumed. In this poster, the team will explain what they have been doing in recent semesters to work towards their goal of testing and preparing this meter for implementation in Zimbabwe this summer, as well as how they have been improving the user experience through website implementation. Funding for this work provided by The Collaboratory for Strategic Partnerships and Applied Research.https://mosaic.messiah.edu/engr2022/1005/thumbnail.jp