Proving # Equilateral Triangles on Sphere

[tainted]

Homework Statement

Ok, I have this problem this week. (1)
<br /> Consider\ a\ tiling\ of\ the\ unit\ sphere\ in\ \mathbb{R}^{3}\ by\ N\ equilateral\\<br /> triangles\ so\ that\ the\ triangles\ meet\ full\ edge\ to\ full\ edge\ (and\ vertex\ to\ vertex).\\<br /> Show\ that\ the\ only\ possibilities\ for\ N\ are\ N = 4,\ N = 8,\ or\ N = 20.

Last week, we had the problem that follows (2)
<br /> Consider\ a\ tiling\ of\ the\ unit\ sphere\ in\ \mathbb{R}^{3}\ by\ equilateral\\<br /> triangles\ so\ that\ the\ triangles\ meet\ full\ edge\ to\ full\ edge\ (and\ vertex\ to\\<br /> vertex).\ Suppose\ n\ such\ triangles\ meet\ an\ one\ vertex.\ Show\ that\ the\ only\\<br /> possibilities\ for\ n\ are\ n = 3,\ n = 4,\ n = 5.

Alright so my problem is that it seems to be nearly the exact same statement except (2) uses n while (1) uses N.

If that is true then wouldn't it be impossible to prove N can only be 4, 8, or 20 if I proved it was only 3, 4, or 5 last week.

Homework Equations

Area of each triangle = 3a - ∏

The Attempt at a Solution

Considering my question isn't for the solution rather than help understanding what it is saying/how this would be possible, I don't have any work yet.

If requested, I can show my answer to (2)

 

[Dick]

Think about using Euler's formula. http://en.wikipedia.org/wiki/Planar_graph#Euler.27s_formula n is the number of triangles meeting at a point, N is the total number of triangles on the whole sphere. They are two different things.

 

[tainted]

Alright thanks man, that's all I needed, I got it!