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 in the space between four densely packed spheres of unit radius arranged in a tetrahedron. Participants emphasize the importance of visualizing the tetrahedron and suggest that drawing it may aid in solving the problem. The conversation highlights the forum's policy on homework questions, indicating that numerical problems or special examples are often categorized as such, requiring users to demonstrate their own efforts before seeking assistance.

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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?
FCC_closed_packing_tetrahedron_(4).jpg
 

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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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