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The mum of three was sentenced at the High Court in Glasgow after pleading guilty to culpable homicide on the grounds of diminished responsibility.
The 47 year old killed twins Austin and Luke and daughter Cecilia at their Edinburgh home last August.
The youngsters' bloodstained bodies were discovered lying side by side at the Slateford Road townhouse following a gas explosion at the building, each with eight stab wounds and multiple abrasions and bruises.
American Riggi was found badly injured after plunging from a second-floor balcony in an apparent suicide bid. She also had stab wounds which were believed to have been self-inflicted.
The court was told previously that Riggi and her estranged husband Pasquale, a Shell UK engineer, had been involved in a legal action over the children's custody at the time of the killings.
Alex Prentice QC, prosecuting, said they had been due to appear at a hearing the day before the youngsters' deaths.
Days before the killings, Riggi told a friend things were so bad he would ``hear about it on the national news''.
On the evening of August 2, Riggi spoke to her husband on the phone. Mr Prentice said she accused him of being in collusion with their solicitors and asked if he would take the children away.
On being told she ``left him no choice'', Riggi replied ``say goodbye then'' and hung up.
She was initially charged with murder but last month admitted three counts of the lesser charge of culpable homicide on the grounds of diminished responsibility.
She was sentenced today at the High Court in Glasgow after Donald Findlay QC spent more than two hours delivering a plea of mitigation on her behalf.