Hi Dreadstar
this is hurting my brain because I don't have the language of maths - I am more a artistic leaning guy than science but I'll try
if it were two lines lying in the same plane, then no because obviously they cross. Now I have found out that you can have a point of intersection between two curves, but again I am thinking that these curves must actually cross each other to 'intersect'. Lets think of two dimensional arcs - you could arange them so as to have a single point of intersection or so as to have two points of intersection.You could also arrange them )( touching but not breaking each other.
Thinking in three dimensions - for spheres - and if intersecting requires cutting the plane - then there is not a point/s of intersection but there is instead a continuous plane of intersection. What I am seeking (and as above I emphasise this is for ideal shapes) is a name (applicable specifically to spheres) where they meet but do not intrude upon one another's planes.
This specific name of this point might not exist, but I find that hard to believe because one a concept is named (so can be learnt) it can be applied more readily to problems. I did look at some explanation of packing tennis balls thinking I might come across what I was looking for.
It's just something I was thinking about and that's surprising in itself

Maybe we have a Mathemetician out there in Mayhemland who is laughing his socks off - I really hope so

Dave