Tetrahedron is the simplest polyhedron, it is just formed from(adsbygoogle = window.adsbygoogle || []).push({}); four triangles, so it has V0=E0=4*3=12, and F0=F=4, of course. Then we find that V0+E0+F0=2(V+E+F) or V0+F0=2V+2F (Because of E0 is always equal to 2E)=4F.

Assume that other polyhedrons are the "evolution" product of a tetrahedron. I mean that they are formed from four triangles of tetrahedron and additional faces such as rectangle, hexagon, etc. For instead, a cube consists of 4 triangles and 4 rectangles. So V0+F0=2V+2F=4(4+a), where a is the number of additional faces. Now let's calculate. It's 32. So we conclude that F0 must be 4.

Finally, we can find Euler Theorem:

2V+2E+2F=V0+E0+4

V+E+F=E0+2

V-E+F=2.

What's your comment about my proof?, I am sorry if you think that it is too poor.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A Proof of Euler Theorem

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**