Polyamory
Polyamory is the practice, desire, or acceptance of having more than one intimate relationship at a time with the knowledge and consent of everyone involved. It is often described as consensual, ethical, or responsible non-monogamy. The word is sometimes used in a broader sense to refer to sexual or romantic relationships that are not sexually exclusive, though there is disagreement on how broadly it applies; an emphasis on ethics, honesty, and transparency all around is widely regarded as the crucial defining characteristic.
While "open relationship" is sometimes used as a synonym for "polyamory" or "polyamorous relationship" the terms are not synonymous. The "open" in "open relationship" usually refers to the sexual aspect of a non-closed relationship, whereas "polyamory" refers to the extension of a relationship by allowing bonds to form (which may be sexual or otherwise) as additional long term relationships.
This term and "friends with benefits" are fairly recent, having come about within the past few decades.
A subset of polyamory is polyfidelity, relationship that use an evenly distributed rotating sleeping schedule that determines who sleeps together and when. In this type of relationship, no one sleeps with anyone outside of those originally involved in the group.
Read more about this topic: Open Relationship