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PLATONIC SOLIDS

Platonic solids are regular geometric solids with regular plane faces.  There are only five platonic solids.  These are the cube, tetrahedron, octahedron, icosahedrons, and dodecahedron.  The number of vertices, edges, and faces for these polyhedrons are as follows:

Polyhedron

Vertices

Edges

Faces

tetrahedron

4

6

4

cube

8

12

6

octahedron

6

12

8

dodecahedron

20

30

12

icosahedron

12

30

20

 

The ancient Greeks has known these five regular solids, each of which have faces that are all identical equal-angled regular polygons the meet at equal angles.  The cube has six faces, each of which is a square.  The tetrahedron has four equilateral triangular faces.  The octahedron has eight equilateral triangular faces.  The icosahedron has twenty equilateral triangular faces.  Lastly, the dodecahedron has twelve equilateral pentagonal faces.

Plato have related these regular solids to the basic elements of nature.  As the lightest and sharpest elements, Plato assigned tetrahedron to represent fire.  The icosahedron was assigned to represent water because of its being fluid and most mobile.  Earth, being the most stable, was assigned to be represented by a cube.  Air, which was light and fluid, was assedgned to be represented by an octahedron.  Finally, Plato assigned dodecahedron, which have the most vertices and edges, and the only one with pentagonal faces, to represent the whole universe.

 

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