Platonic Solids

Mehmet Kemal ERSeray ARSLAN

What is "Platonic

Solids" ???

What is "Platonic Solids" ???Five regular solids →

Platonic SolidsFive regular solids:

equal sides equal regular faces

Tetrahedron Oktahedron lcosahedron Hexahedron Dodecahedron

TetrahedronA tetrahedron has 4 equal triangle faces.

OctahedronAn octahedron has 8 equal triangle faces.

IcosahedronAn icosahedron has 20 equal triangle faces.

HexahedronA hexahedron (cube) has 6 equal square faces.

DodecahedronA 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

Referenceshttp://www.mathsisfun.com/geometry/platonic-solids-why-five.html

http://www.mathsisfun.com/platonic_solids.html

Thanks for your attention