Eaton’s body was found around 60 meters inside the cave beneath an air shaft which had been covered by a large wooden pallet, Lagoudakis added.
Eaton was attending a conference at the Orthodox Academy in Crete and is believed to have disappeared during a run.
The police said on Wednesday that Eaton was asphyxiated. Minor stab wounds were also found on her body, but police said they were not believed to be the cause of her death. The police believe the body was dumped inside the cave, because it was found face down.
Lagoudakis told CNN on Thursday that he had never seen a case like this in his four years as police chief.
Relatives — including her mother, son and siblings — released tributes to her on Thursday.
Eaton’s sister praised her great range of achievements describing her as an “accomplished woman” of “insatiable curiosity.”
“She took great pleasure in preparing exquisite meals and had an exotic fashion sense. She loved perfume. She taught and practiced Tae Kwon Do as a second degree black belt. She finished crossword puzzles way too quickly, played concertos, and read extensively. She fit Jane Austin’s strictest description of an ‘accomplished woman’ while maintaining a natural humility and ‘insatiable curiosity’,” her sister wrote.
Her sister added that Eaton would often worry about not giving her family enough time as well as devoting herself to science.
She continued, “But anyone who read of her accomplishments in the field of molecular and developmental biology, or who witnessed her joy in tutoring, comforting, and inspiring her children, or sharing with, and loving her husband, would not have suspected. With a deep sensitivity and compassion, she somehow made us all a priority.”
The statements were released on a website set up by Eaton’s employer, the Max Planck Institute at Dresden University in Germany.
Her family initially believed Eaton, a regular runner, likely died during a run as a result of heat exhaustion or a fall in the rough terrain.
The horrific details surrounding Eaton’s death have shocked the locals, some of whom thought she died in a hiking accident. Crete is known to be among the safest of the Greek islands despite its size and the large number of tourists.
“We are deeply shocked and disturbed by this tragic event,” the Max Planck Institute said in a statement. “Suzanne was an outstanding and inspiring scientist, a loving spouse and mother, an athlete as well as a truly wonderful person beloved to us all.”
Eaton was the wife of British scientist Tony Hyman and mother of two sons, according to institute.