[3][4] In 1965, he received a QEII Arts Council Travel Grant, which he used to study lost-wax casting in Europe.

[2] By the 1970s, Twiss began focusing on creating works that sound freestand within gallery spaces.

[8] He has participated in many exhibitions including Volume and Form, Singapore; Content/Context at Shed 11 - Museum of New Zealand Te Papa Tongarewa;[9] and Aspects of Recent New Zealand Art, Auckland City Art Gallery.

His work, Flight Trainer for Albatross, stands at the entrance of the Auckland viaduct on Princes Wharf.

[5] In the 2002 Queen's Birthday and Golden Jubilee Honours, Twiss was appointed an Officer of the New Zealand Order of Merit for services to sculpture,[12] and in 2011 he received an Arts Foundation Icon Award.