The Platonic Solids

Index of Contents
A brief review of some geometry concepts.
The solids and their magic.
A taste of their history.

1. A brief review of some geometry concepts
Polygons: you know them very well!
Closed figure maded with segments.
Examples: triangles, quadrangles, pentagons, hexagons...
Regular polygons : every side has the same length.

1. A brief review of some geometry concepts
Polyhedrons: we move on 3-D
Three-dimentional closed figure made with polygons.
Its parts are called: vertex, edges and faces.
Prisms and Pyramids are polyhedrons.

2. The platonic solids and their magic
There is an unlimited number of different polyhedrons.
But...how many polyhedrons can we built on condition that:
we use only one kind of regular polygon
and
we must have the same number of edges in each vertex ?
Only the 5 platonic sòlids!

Here you have them : Tetrahedron, Hexahedron/Cube, Octahedron, Dodecahedron, Icosahedrom
Tetra = 4 Dodeca = 12
Octa = 8 Icosa = 20
Hexa = 6 Hedron = Face

It’s interesting to note that:
Because of their symmetry , they all can include and be included in a sphere.
They all 5 carry out Euler’s Formula
Vertex – Edges + Faces = 2

3. A taste of their history
They have been known since antiquity.
Carved stone balls from Scotland (400 aC)
Plato wrote about them in the Timeus (360 bC)

Ancient Greeks connected them with the four classical elements
and the Universe/Divinity .

In the 16th century, Kepler tried to link them with the 5 known planets but later he had to give up the idea.

Finally, artists of all time have been fascinated by the perfection of their shapes:
Da Vinci Dürer

Escher Dalí

Epilogue
I hope you have enjoyed the speech and I encourage you to look for the platonic solids wherever you go!!!
Thank You!

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The Platonic Solids

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