Twyman died Wednesday from blood cancer, his family said.
Twyman scored 1,598 points and had 1,242 rebounds at Cincinnati before he was the eighth-overall selection in the 1955 NBA draft.
He was drafted by Rochester and stayed with the team when it moved to Cincinnati. He averaged 19.2 points and 6.6 rebounds a game in his pro career from 1955-66. The Sacramento Kings, where the franchise is currently located, retired his jersey No. 27.
Twyman averaged 31.2 points a game in 1959-60, becoming the first NBA player to average more than 30 points a game.
He was selected to the NBA All-Star team six times and was inducted into the Naismith Basketball Hall of fame in 1983.
"The Bearcat family lost one of our legends yesterday with the passing of Jack Twyman," said Cincinnati Director of Athletics Whit Babcock.
"He was a true gentleman, a great man who loved UC. He will be missed. He supported his alma mater in every facet. He was an icon. The name 'Jack Twyman' will forever be associated with our university and a golden era of UC athletics."