http://ie.technion.ac.il/~onn/Selected/JCO07.pdf maybe (uses an LP oracle) and ftp://ftp.ifor.math.ethz.ch/pub/fukuda/reports/polyfaq040618.pdf . The latter one mentions polytopes too. Dunno how over-determined your system is. If a lot, then it should be reduced to a minimal one as the first step...