Petrie Polygons of a Polyhedron - Universal Hyperbolic Geometry

Explore the fascinating world of Petrie polygons and polyhedron tesselations in this 26-minute video lecture. Delve into the discoveries of John Flinders Petrie, examining the unique polygonal paths on polytopes and polyhedra, with a focus on their remarkable properties when projected onto specific planes. Learn about regular tesselations, including the three famous examples in the plane, and understand the Schlafli symbol. Investigate the Platonic solids, their Petrie polygons, and the differences between perspective and orthogonal projections. Examine in detail the Petrie polygons for both the cube and dodecahedron, gaining insights that will prove valuable when extending these concepts to hyperbolic geometry.

Introduction tesselation of a surface
Regular tesselations
The three regular tesselations of the plane
The platonic solids and their Petrie polygons
Perspective and orthogonal projections
Petrie polygon for a cube
Petrie polygon for the dodecahedron