Dimitry, citing Plato’s Symposium on Love:
It might be irrelevant here, but the term “Platonic Love” comes from Plato’s famous philosophical dialog “Symposium” (A MUST reading for any thinking person). In that dialog Plato gives probably the only definition of love in the history of human thought that can be considered as valid. Platonic Love is the complete realization of the unity of souls between the two human beings, in which they both perceive God in each other. This kind of love means complete trust, complete self-sacrifice, complete compassion, complete mutual belonging, and it can occur between two people of any gender as sexual partners or friends. So in the state of Platonic Love sex is an option but not a requirement, therefore essentially the Platonic Love can either take a form of deepest friendship or deepest romantic relationship. Therefore, the Platonic Love is the highest achievable form of friendship AND sexual love equally, the absolute form of love achievable in the material world, and as you can see, it has nothing to do whatsoever with a situation when the two people hardly know each other and make small talk.