The Platonic Solids

Index of Contents

1. A brief review of some geometry concepts.2. The solids and their magic.3. 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!

2. The platonic solids and their magic

• Here you have them: Tetrahedron, Hexahedron/Cube, Octahedron, Dodecahedron, Icosahedrom

Tetra = 4 Dodeca = 12Octa = 8 Icosa = 20

Hexa = 6 Hedron = Face

2. The platonic solids and their magic

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)

3. A taste of their history

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

3. A taste of their history

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

3. A taste of their history• Finally, artists of all time have been fascinated by the perfection of

their shapes:

Da Vinci Dürer

3. A taste of their history

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!