Platonic Solids and Their Symmetries - Dynamics on Graphs 10

Explore the fascinating world of Platonic solids and their symmetries in this 26-minute video lecture from the "Dynamics on Graphs" series. Delve into the tabulation of familiar Platonic solids and their symmetry groups, examining both rigid motions (focusing on rotations) and reflections. Gain insights into how this knowledge serves as a foundation for understanding exceptional structures in mathematics and physics. Discover the enticing connections between 4-dimensional versions of these regular solids and particle physics, string theory, and various algebraic objects. Learn about the approach of obtaining these exceptional objects through simple dynamical games on graphs, particularly the Mutation Game and Mozes' Numbers Game. Connect these symmetries to graph theory and extend the understanding to 4-dimensional regular solids. Perfect for motivated amateur or professional mathematicians seeking to explore research-level mathematics without excessive abstraction and complexity.

Introduction
Platonic solids
Tetrahedron
Rigid motions
Rotations
All Symmetries
The alternating group