They like to build up their own libraries and meaningful web pages. The basic principle of intellectual freedom is to be able to buy any book you like. Of course, this freedom requires not only a bit of money, as well as parental consent perhaps, but also the ability to read and understand what you have picked up and hold before you. Polymaths strive for the freedom to read many kinds of difficult books. This is real freedom, the freedom to understand what you want.
Polymaths also like to play with computers, to make things.
They are often artists, musicians, puppeteers etc. They like to get involved in cultural and scientific fairs, as long as they are not forced into it. Polymaths do not like to be forced to do anything. They tend to be intellectually rebellious. But they usually catch up on their school work in the nick of time because they read and write well, which is the real key to academic success.