- #1

tainted

- 28

- 0

## Homework Statement

Ok, I have this problem this week.

**(1)**

[tex]

Consider\ a\ tiling\ of\ the\ unit\ sphere\ in\ \mathbb{R}^{3}\ by\ N\ equilateral\\

triangles\ so\ that\ the\ triangles\ meet\ full\ edge\ to\ full\ edge\ (and\ vertex\ to\ vertex).\\

Show\ that\ the\ only\ possibilities\ for\ N\ are\ N = 4,\ N = 8,\ or\ N = 20.[/tex]

Last week, we had the problem that follows

**(2)**

[tex]

Consider\ a\ tiling\ of\ the\ unit\ sphere\ in\ \mathbb{R}^{3}\ by\ equilateral\\

triangles\ so\ that\ the\ triangles\ meet\ full\ edge\ to\ full\ edge\ (and\ vertex\ to\\

vertex).\ Suppose\ n\ such\ triangles\ meet\ an\ one\ vertex.\ Show\ that\ the\ only\\

possibilities\ for\ n\ are\ n = 3,\ n = 4,\ n = 5.[/tex]

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)**