That the kissing number of a sphere in dimension 3 is 12 is well known. However, it is also known that there is a lot of empty space between the 12 spheres. I deduce (am I wrong?) that there are many different ways (configurations) of 13 spheres such that a central one is in contact with the remaining 12.

Is anyone aware of an algorithm that can be used to generate such configurations? Of course, one could go by trial end error. I was looking for something more efficient, elegant and intelligent than just "try to put them in some way until there are no overlaps".

Thank you.

That the kissing number of a sphere in dimension 3 is 12 is well known. However, it is also known that there is a lot of empty space between the 12 spheres. I deduce (am I wrong?) that there are many different ways (configurations) of 13 spheres such that a central one is in contact with the remaining 12.

Is anyone aware of an algorithm that can be used to generate such configurations? Of course, one could go by trial end error. I was looking for something more efficient, elegant and intelligent than just "try to put them in some way until there are no overlaps".