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The Remarkable Platonic Solids I - Universal Hyperbolic Geometry

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This introductory lesson examines the five Platonic solids through their symmetry, history, Euclid’s formulas, and Euler’s fundamental relation for polyhedra. It also presents a Platonic solid as a regular tiling of the sphere.

Syllabus

Introduction
Symmetrty properties
Platonic solids are examples of polyhedra
History of the Platonic solids
Euclid: Book 13 of The Elements
Formulas that Euclid derived
Euclid proved there are 5 regular solids
L. Euler's fundamental relation for polyhedra
A platonic solid viewed as a regular tiling of the sphere

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Insights into Mathematics

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