Canonical Structures Inside the Platonic Solids - Tetrahedron Symmetry - Lecture 49

Explore the hidden symmetries within Platonic solids, focusing on the tetrahedron's surprising three-fold symmetry embedded in its four-fold structure. Delve into the geometric properties of opposite edge pairs, uncover the relationship between "three-ness" and "four-ness," and examine the tetrahedron's symmetries. Gain insights into group theory concepts, particularly the symmetric group S3, as you investigate these canonical structures. Learn how these geometric insights contribute to a deeper understanding of the tetrahedron's symmetries and their connections to abstract algebra.

The tetrahedron
There are 3 pairs of opposite edges
Geometrical approach to a pair of opposite edges
Three-ness from four-ness
Symmetries of the tetrahedron
The symmetric group S3