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Math Help - A cube and its vertices

  1. #1
    Newbie
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    Auckland, NZ
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    Wink A cube and its vertices

    Given a cube, how many acute angles triangles are there whose vertices are of vertices that cube?

    Is there a simpler way to solving this?
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, clarebear14!

    Given a cube, how many acute-angled triangles are there
    whose vertices are vertices of that cube?

    Is there a simpler way to solving (Thinking) this?

    We find that most triangles are right triangles.

    The exceptions are eight equilateral triangles
    . . formed by the diagonals of the faces.


    Code:
                  *---------o
                /     o   / |
              /   o     /   |
            / o       /   o |
          o---------*       |
          | o       |   o   *
          |   o     |     /
          |     o   | o / 
          |       o | /
          *---------o
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