Triangle on a Sphere Question Interpretation

[tainted]

Homework Statement

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
$n=3$, $n = 4$, or $n=5$

Homework Equations

The Attempt at a Solution

I guess the main thing I need help with is interpretation of the question.

Thank you

 

[HallsofIvy]

A (flat) triangle won't fit on the surface of a sphere. Do you mean spherical triangles?

 

[Dick]

Hint: there's a relation between the angles of a triangle and it's area. Figure out the area of a triangle if n of them share a vertex. How many will fit on a sphere? If you think about there is also a easy correspondence between these and some of the platonic solids.