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|Olympic medal record|
|1922 Ljubljana||Individual all-round|
|1926 Lyon||Individual all-round|
|1922 Ljubljana||Team all-round|
|1926 Lyon||Team all-round|
|1922 Ljubljana||Pommel horse|
|1930 Luxembourg||Pommel horse|
Šumi was born in Kranj. He took part in three World Championships in gymnastics for Yugoslavia. At the 1922 World Championships in Ljubljana, he was part of the Yugoslav team that took silver in the team event, behind Czechoslovakia. He also took gold in the individual combined event, as well as gold in the rings, horizontal bar, and parallel bars, and silver in the pommel horse.
At the next World Championships, in Lyon, France in 1926, he again took silver in the team event, again behind Czechoslovakia. Sumi won the individual combined event for the second time, but won no apparatus medals on this occasion.
His last World Championship medal came in 1930, at the World Championships in Luxembourg, where he took silver in the pommel horse. He died in Vienna.
Sumi was the only gymnast to have taken individual overall medals in consecutive World Championships until the Chinese gymnast Yang Wei achieved it in 2006 and 2007. Additionally, Sumi is one of only two repeat male World All-Around Champions (of which there are 7) in the sport of Artistic Gymnastics, along with Yuri Korolyov, never to make an Olympic appearance as a competing athlete.