It was not called Unicon; that name was invented (by Meryl Shaffer of the National Circus Project) for the second one. This one was called International Unicycling Convention!
There were about 100 competitors; about 20 from Japan and a total of about 7 countries represented, including Anmon Mier, grandson of Golda Mier, from Israel.
First World Champions of Individual Freestyle: Teresa Hemminger (Abrahams), USA and Peter Rosendahl, Sweden. To win the Individual title, riders had to get the best combined score in a Compulsory event along with their Freestyle performance. It was an early version of the Standard Skill event that followed in later years.
Pairs Freestyle: Deborah Jones and John Foss, USA
Group: Team Japan (the only entry)
Track: there was no combined title in those days. The races were run in meters, for the first time in the US.
Basketball: Puerto (vs. Semcycle. there was just one game, squeezed in during the dinner break)
Read more about it, in the USA Newsletter that followed the convention. This was the last one I did for the USA Inc; after that I switched to the IUF Newsletter, which came our famously late…