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Homework Help: Triangle on a Sphere Question Interpretation

  1. Sep 17, 2012 #1
    1. The problem statement, all variables and given/known data
    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##

    2. Relevant equations

    3. The attempt at a solution
    I guess the main thing I need help with is interpretation of the question.

    Thank you
  2. jcsd
  3. Sep 17, 2012 #2


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    Science Advisor

    A (flat) triangle won't fit on the surface of a sphere. Do you mean spherical triangles?
  4. Sep 17, 2012 #3


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    Homework Helper

    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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