Detectives released details of the shocking crime on Friday, hours after a court revoked an order suppressing the identity of Tamika Sueann Rose Chesser.
She is charged with murdering Julian Story, 39.
Magistrate Ben Sale on Friday lifted a restriction on the publication of her name or image.
The 34-year-old former Beauty and the Geek contestant 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.
His body was dismembered following his murder, Detective Superintendent Darren Fielke revealed.
"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 South Australia Police major crime chief told reporters.
"I can only imagine, and I want you to imagine, the grief this news is causing.
"Julian's family ... are devastated by his loss and the circumstances surrounding his death.
"It is crucial that we locate Julian's head so that his family has the opportunity to allow him to rest."
Police released still images and video of the alleged murder that were recorded after the killing, which investigators said occurred about midnight on June 17.
The images show a woman wearing a black headscarf and black full-body coverings.
"She often walked with one, two or three dogs, she walks through back streets, she walks through parks in the Port Lincoln area," Det Supt Fielke said.
Officers want to pinpoint Chesser's movements between midnight on June 17 and the afternoon of June 19 and asked residents to review any CCTV and dash cam footage.
In a statement, the Story family said they were "navigating an unimaginable loss".
"We are also deeply grateful to our family and friends and this extraordinary community whose kindness and support have helped carry us through," they said.
"Your prayers, presence, and quiet strength mean more than words can say."
Chesser, who appeared in court via video link on Friday, has been refused bail since her arrest.
She is being held under order at a forensic mental health facility.
The now-lifted suppression order also prevented publication of Mr Story's name and details of the alleged crime.
Police found Mr Story's body after firefighters were called to the Flinders Highway property to investigate reports of a blaze.
There was no information to suggest drugs were involved, but both the victim and accused were known to police, Det Supt Fielke said.
Mr Story was a long-time resident of Port Lincoln and he had been in a relationship with Chesser for "at least a few months", he added.
"We know they were in a relationship, and I'm not suggesting that's a motive, but it's something that's been explored … there's no obvious motive that we are aware of at this point," Det Supt Fielke said.
Chesser will re-appear in court for a committal hearing in December.
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