Largest sphere in the space between dense packed spheres

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iantresman
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If I consider a tetrahedron of four densely packed spheres of unit radius, what it the radius of the largest sized sphere that can fit in the space in between?
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Well, since this is PF, the inevitable reply is: what did you do so far to find it ?
Did you alredy draw the tetrahedron in the usual manner (lines) ?
 
I didn't know where to start, whether drawing a tetrahedron and 2D circles is relevant.
 
If you have a better idea, follow that !
 
Thread closed, as it is a homework type question.

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