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MEASUREMENT
Lesson 3 - Page 2

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Plato believed that the four basic elements of matter were earth, water, air, and fire.  Earth was associated with the stable cube, fire with the simple but pointy tetrahedron, air with the mobile appearance of the octahedron, and water with the multifaceted icosahedron.  The dodecahedron was associated with the universe as all the other shapes fit inside.  Johannes Kepler even tried to use these shapes when he was developing his planetary movement theories.  He soon found out that the Universe was not that simple, and this motion theory had to be abandoned. 

These shapes are known as the Platonic solids which are polyhedrons that have the same identical face and are equilateral and all the solids can be circumscribed by a sphere (with their vertices within the sphere.  The Platonic solids includes the tetrahedron (four triangular faces), hexahedron or cube (6 square faces),  the octahedron (8 triangular faces), the dodecahedron (12 pentagonal faces) and the icosahedron (20 triangular faces).


Icosahedron (20 faces)


Hexahedron (6 faces)


Tetrahedron (4 sides)


Dodecahedron (12 faces)

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