Thomas Tamatea Ariki-Nui McGregor, 31, was sentenced in the High Court at Wanganui this morning.
McGregor had earlier admitted murdering his 2-month-old daughter Hinekawa who died on January 12, 2012 in Wanganui Hospital.
A post-mortem examination found she had suffered a deliberate head injury.
McGregor also faced a wounding with reckless disregard charge relating to another of the triplets, to which he also pleaded guilty.
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.