Detectives released details of the shocking crime on Friday, hours after a court revoked an order suppressing the identity of Tamika Sueann-Rose Chesser, who is charged with murdering Julian Story, 39.
In Adelaide Magistrates Court on Friday, Magistrate Ben Sale lifted the order that prevented the name and image of reality TV contestant being published.
The former Beauty and the Geek contestant, 34, was arrested on June 19 after Mr Story's body was found at the couple's home at Port Lincoln, on South Australia's Eyre Peninsula.
At a media conference, Detective Superintendent Darren Fielke said Mr Story's body was dismembered after he was murdered.
"And while I won't provide any further detail about that at this time, I can tragically say that we have not recovered the head of Julian Story," the major crime chief said.
"I can only imagine, and I want you to imagine, the grief this news is causing Julian's family.
"Recovering Julian's head to return it to his family so they can have a peaceful outcome, have a funeral and lay him to rest is a really important aspect for us."
Chesser is also charged with disposing of human remains to pervert the course of justice and assaulting a police officer.
Police released still images and video of Chesser recorded after the murder, which allegedly occurred at mignight on June 17.
"I'm appealing to local residents to review CCTV or dash cam footage which they may have, which may assist the investigation," Supt Fielke said.
"Specifically, we are seeking to identify the movements of Tamika, particularly between midnight Tuesday 17 June until the afternoon of Thursday 19 June."
Chesser, who appeared in court via video link on Friday, was refused bail when she first appeared last week and is being held under a mental health detention order.
Mr Sale lifted the suppression order, which had also prevented the publication of Mr Story's name, the alleged circumstances of his death and the investigation.
Chesser will reappear at a committal hearing in December.
Police found Mr Story's body after firefighters were called to the Flinders Highway property to investigate reports of a blaze.
After Chesser's arrest, SA Police Assistant Commissioner Ian Parrott said there were a lot of unanswered questions in the investigation and it was a complex crime scene "so it will take some time to understand the exact nature of what's occurred".
In 2010, Chesser finished second in the second series of the reality TV show Beauty and the Geek, in which "beauties" and "geeks" seek love and a cash prize.
Her Instagram profile says she is a model and actress.
Lifeline 13 11 14
beyondblue 1300 22 4636
