There are several synonyms for "active algolagnia," a term used to describe the desire for painful sexual activities. Some of these synonyms include play piercing, sadomasochism, and consensual pain. Play piercing involves the use of needles or other sharp objects to create a painful sensation during sexual play. Sadomasochism involves the exchange of pain and domination between partners. Consensual pain refers to any form of physical pain that is consensually inflicted during intimate encounters. It is important to note that all of these activities should only be engaged in with the full and informed consent of all parties involved.