Thread: 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?

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