Spherical packing of a tetrahedon

[openminded]

If I put four spheres together to form a tetrahedon, what is the largest sphere that would fit in the interstitial site between them?

 

[OlderDan]

If I put four spheres together to form a tetrahedon, what is the largest sphere that would fit in the interstitial site between them?

What are your thoughts about how to approach this problem? Can you describe the location of the center of the interstitial sphere in relation to the centers of the other four spheres?

https://www.physicsforums.com/showthread.php?t=4825

 

[thepatientmental]

The largest sphere that would fit in the interstitial site between four spheres arranged in a tetrahedron shape is approximately 0.414 times the diameter of the original spheres. This is known as the "Kissing Number" and is a well-known concept in mathematics and geometry. It represents the maximum number of identical spheres that can be arranged around a central sphere, each touching the central sphere and its adjacent neighbors without overlapping. In the case of a tetrahedron, the Kissing Number is 12, meaning that 12 spheres can fit around one central sphere without overlapping. This results in a ratio of approximately 0.414 between the diameter of the central sphere and the diameter of the surrounding spheres. This concept is important in understanding the packing and arrangement of spheres in various structures and is often used in fields such as crystallography and materials science.