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Platonic Solids

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.

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Platonic Solids

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  1. PlatonicSolids Mehmet Kemal ER Seray ARSLAN

  2. What is "PlatonicSolids" ???

  3. What is "PlatonicSolids" ??? • Fiveregularsolids→PlatonicSolids • Fiveregularsolids: • equalsides • equalregularfaces

  4. Tetrahedron • Oktahedron • lcosahedron • Hexahedron • Dodecahedron

  5. Tetrahedron • A tetrahedron has 4equaltrianglefaces.

  6. Octahedron • An octahedron has 8equaltrianglefaces.

  7. Icosahedron • An icosahedron has 20 equaltrianglefaces.

  8. Hexahedron • A hexahedron (cube) has 6equalsquarefaces.

  9. Dodecahedron • A dodecahedron has 12regular pentagon faces.

  10. 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.

  11. 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 Edgesalways equals 2 Itis written: F + V - E = 2

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

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

  14. Thanksforyourattention

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