Why is tetrahedral the most stable?

[Abhijeet Verma]

How do we prove that tetrahedral arrangement is the arrangement which allows 4 points to be maximum apart from each other about a fixed centre, assuming that the points are all symmetrical about the centre.
(I am asking in context of the structures of the molecules like CH4, since there the structure is favoured since it allows the individual atoms to be maximum apart and hence minimise repulsion)

 

[Vanadium 50]

How do we prove that tetrahedral arrangement is the arrangement which allows 4 points to be maximum apart from each other about a fixed centre, assuming that the points are all symmetrical about the centre.

Any four points determine a tetrahedon.

 

[Abhijeet Verma]

Sorry, by tetrahedral arrangement, i mean a tetrahedral with an angle of nearly 109deg. 28 min.

 

[Bystander]

Regular tetrahedron.