Triangle on a Sphere Question Interpretation

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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
 

Answers and Replies

  • #2
HallsofIvy
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A (flat) triangle won't fit on the surface of a sphere. Do you mean spherical triangles?
 
  • #3
Dick
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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.
 

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