Justice Ronald Young told McGregor it "is difficult to understand how you came to this. You had a good family background, no drugs or alcohol issues and you were involved with your culture.
"You had good family support if you felt the situation was getting out of your control.''
Justice Young said the victim impact report was about deep sadness and ``that you had it in you to kill your child''.
"You will carry the scar of this offending for your life and so you should.
"It is terrible offending and shocking to read.''
The court heard that McGregor began a relationship with Tiffany Topia in 2009 and the triplets, all girls, were born by caesarean section in Wellington Hospital on November 9, 2011.
The babies were later moved to Wanganui Hospital and discharged on December 3.
From then until December 21 the family lived with the defendant's parents in Waitotara.
They later moved to Wanganui.
The court heard that on at least four occasions McGregor forcefully shook one of the other triplets, causing at least four subdural haemorrhages.
Hinekawa, the second born of the triplets, spent significant periods after being discharged with other family members to give the accused and Ms Topia a break, the court heard.
On January 12 at 11.47am, McGregor sent a text message to Ms Topia saying Hinekawa was at home, with the other two babies.
The court heard that within the next hour McGregor went into the triplets' bedroom and picked Hinekawa up out of her cot.
He either swung or threw Hinekawa against a wall, the floor or another object, causing a fracture to the right hand side of her skull and a significant bilateral subdural hematoma.
She immediately became lifeless and attempts to revive her failed.
McGregor sent a text at 12.46pm telling Ms Topia to return home ``now'' as something was wrong with Hinekawa.
When she did she was met by McGregor carrying Hinekawa out of the house and they took the child to Wanganui Hospital.
She was pronounced dead at 1.10pm.
In a statement, the family of Hinekawa Topia-McGregor said: "We take each day as it comes and stay strong for our children because we love them. Even though we no longer have Hinekawa with us, we love her just the same, and we think about how we are going to tell her siblings what happened to her. We know they will have questions when they are older and much like we do now; we will try to answer them.
"The life of our Hinekawa has been taken away and this will continue to affect us for the rest of our lives. Every time we look at the girls we are reminded that we have one living with the angels in heaven.''
