2-methylpropene is bubbled into dilute sulfuric acid at room temperature, it appears to dissolve. what's new?

The reaction would be a cationic polymerization catalyzed by the protonation of the 2-methylpropene by the sulfuric acid to give a tertiary carbocation which would then be attacked by the electron-rich double bond of another 2-methylpropene forming another carbocation, etc. etc. The polymer would eventually precipitate as it grew.