Question 194454
I don't understand Euler's Law, v+f=e+2

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Euler's formula holds for every solid figure consisting of
vertices, flat faces, and straight edges.

For any solid figure with only flat surfaces and 
straight edges, this formula always holds:

Number of vertices + number of faces = number of edges + 2

Here is a demonstration of that formula with a "box",
that is, a rectangular solid:

{{{drawing(400,400,-1,5,-1,5, line(3,2,4,3),
rectangle(0,0,3,2), rectangle(1,1,4,3), line(0,2,1,3),
 line (3,2,4,3), line(0,0,1,1), line(3,0,4,1),
locate(0,0,A), locate(3,0,B), locate(2.9,2.3,C), locate(-.1,2.3,D),
locate(1,1,E), locate(4,1,F), locate(4,3.3,G), locate(1,3.3,H)
 )}}}


Count the vertices (sharp corners).  They are 

A, B, C, D, E, F, G, H

That's 8.  So for the above figure, v = 8

-----

Count the faces (flat surfaces).  They are rectangles 

ABCD, EFGH, AEHD, BFGC, ABFE, DCGH, 

That's 6.  So for the above figure, f = 6

-----
  
Count the edges.  They are line segments: 

AB, BC, CD, DA, EF, FG, GH, HE, AE, BF, DH, CG

That's 12.  So for the above figure, e = 12

-----

Now look at Euler's formula:

{{{v+f=e+2}}}

Substituting,

{{{8+6=12+2}}}

{{{14=14}}}

So you see that Euler's formula holds for the
above rectangular solid.

Euler's formula holds for every solid figure consisting of
vertices, flat faces, and straight edges.

Edwin</pre>