Detectives have released a photograph of a curtain identical to the one which was found wrapped around a torso discovered on a beach.
The torso of 30-year-old David Guy was found by a group of foreign students on Southsea beach, Portsmouth, in front of The Pyramids, shortly before 5.30pm on Tuesday, Hampshire Constabulary said.
The lower half of what appears to be Mr Guy's body was found on the rocks at low tide in front of Castle Field, Southsea, by police search teams shortly after 8am on Friday, a police spokeswoman said.
Mr Guy had no fixed address but was believed to have been staying in the Southsea area before his death.
Hampshire Constabulary is trying to establish the origins of the pink Wilkinson-own brand Wilko kids curtain and is appealing to anyone who may have thrown theirs out, sold a pair or knows of somebody who has replaced theirs, to come forward.
Detective Chief Inspector Dick Pearson, senior investigating officer, said: "I'm particularly keen to hear from anyone who has thrown out a pair of these curtains recently or maybe knows of someone who has. Equally, someone you know may have taken theirs down suddenly. If so, we want to hear from you."
Detectives are appealing for any information about Mr Guy and would like to speak to his friends and associates.
A post-mortem examination conducted on Wednesday evening failed to determine a cause of death but police believe Mr Guy suffered a "sustained and violent assault".
Mr Pearson said: "We are keen to gather as much information as possible about Mr Guy - even the smallest piece of information could be crucial so please do get in touch." Anyone with any information which may help with the investigation should contact the Eastern Area Major Investigation team on 101, quoting Operation Nimbus, or Crimestoppers, anonymously, on 0800 555111. Mini-Com users can call police on 01962 875000.
A 46-year-old man from Southsea, who was arrested on Thursday on suspicion of murder, remains in police custody. Magistrates have granted detectives until Sunday evening to question him. Richmond Road in Southsea remains sealed off and is likely to remain so for some time, the police spokeswoman said.