I Largest sphere in the space between dense packed spheres

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The discussion centers on determining the radius of the largest sphere that can fit between four densely packed unit spheres arranged in a tetrahedron. Participants emphasize the importance of demonstrating prior efforts to solve the problem, as it is categorized as a homework question. Drawing the tetrahedron and considering 2D circles are suggested as potential starting points, though clarity on their relevance is questioned. The thread is ultimately closed due to its classification as a homework-type inquiry. Users are reminded to follow the homework template for better assistance.
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.

A reminder: To qualify as homework merely the problem itself is taken into account, not its real life origin, which we cannot know anything about. So if a problem is of numerical nature or involves an otherwise special example, then it's likely homework. We request our users of the homework section to use and fill out the template, which will automatically be inserted there, esp. part 3, which covers own efforts. It helps us a lot in order to solve the obstacles the user might have.

Thank you.
 

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