Say I have N nodes linked to each other by a flexible cable of constant radius R (even when making knots of it), how do I know the minimum volume for a complete interconnectivity (i.e. each node being connected to all other nodes by one bidirectional cable)? Obviously, given the thickness of the cable, each node must also have a size big enough to allow every cable to plug in.
Nodes may be spherical but this is not mandatory.
This is not homework.
I have no idea where to start from. I can compute the number of cables, i.e. N times (N-1), and possibly the minimum surface of a node, i.e. R squared times Pi times (N-1) but this is approximative as circles cannot be perfectly packed.
More difficult here, is the packing of all these cables in tridimensional space. I could do it one by one, numerically, but I wonder if there is a more analytical approach to this.
Note that the position of the nodes can be freely choosen. They do not need to be located on the shell.
I did not find duplicates but I am not sure I use the right keywords.