Mehmet Kemal ER Seray ARSLAN Platonic Solids Mehmet Kemal ER Seray ARSLAN

What is "Platonic Solids" ???

What is "Platonic Solids" ??? Five regular solids → Platonic Solids Five regular solids: equal sides equal regular faces

Tetrahedron Oktahedron lcosahedron Hexahedron Dodecahedron

Tetrahedron A tetrahedron has 4 equal triangle faces.

Octahedron An octahedron has 8 equal triangle faces.

Icosahedron An icosahedron has 20 equal triangle faces.

Hexahedron A hexahedron (cube) has 6 equal square faces.

Dodecahedron A dodecahedron has 12 regular pentagon faces.

Platonic Solids - Why Five? In a nutshell, it is impossible to have more than 5, because any other possibility would violate simple rules about  the number of edges, corners and faces you can have together.

Euler's Formula Do you know about "Euler's Formula"? It says that for any convex polyhedron (which includes the Platonic Solids) the Number of Faces plus the Number of Vertices (corner points) minus the Number of Edges always equals 2 It is written:   F + V - E = 2

Try it on the cube: A cube has 6 Faces, 8 Vertices, and 12 Edges, so: 6 + 8 - 12 = 2

References http://www.mathsisfun.com/geometry/platonic-solids-why-five.html http://www.mathsisfun.com/platonic_solids.html

Thanks for your attention 