(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

Area of each triangle = 3a - ∏

3. 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)

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# Homework Help: Proving there can only be certain amounts of eq. triangles on sphere with same verte

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