(Platonic-ness? Platonicness? Platonicy? Platonicity? I don't know.)

Ahhhhhhhhh! I feel like I'm going insane! Too many word choices! *runs head first into wall* For what it's worth, I vote for platonicity though. It sounds almost real ;)

Pretty soon the facade is going to crack though, they are enjoying the touching way too much to keep up the platonicity guise for much longer!