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Question 544815: Hello,
I am trying to imagine using three flash lights in a ball to light it up without changing the balance of the ball (too much). If the end of each light is at the center, could they be positioned to be equidistant from each other?
If it were just a single plane, then the angle between each would be 120 degrees. How should two be rotated along other planes to have the ends be equidistant in space?
Thanks!
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! I am trying to imagine using three flash lights in a ball to light it up without changing the balance of the ball (too much). If the end of each light is at the center, could they be positioned to be equidistant from each other?
If it were just a single plane, then the angle between each would be 120 degrees. How should two be rotated along other planes to have the ends be equidistant in space?
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This is 3 points on a sphere that are equidistant, and have a CG at the center of the sphere.
Any placement of 3 points in space determines a plane, so the 3 points will always be in the same plane, the plane they define. If their CG is the center of the sphere, then the 3 points have to be on an equator (or great circle) of the sphere, so they have to be spaced 120 degrees apart.
That meets the criteria, and gives the maximum distance between any 2 points.
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If you have 4 points, they're the points of a regular tetrahedron.
6 points is the inscribed octahedron.
8 is the inscribed cube.
12 is the icosahedron.
20 is the dodecahedron.
I don't think others are possible.
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