if you've only found 12, i think you're missing the general idea. all you have to do to get to the majority is follow all the trade lanes. otherwise you have to find jump holes, which can usually be found by looking at patrol route maps, or getting hints or outright buying the locations at bars.

There's 52 systems total, including all the dangerous "border world" systems, which are the Omega, Sigma, Tau, and Omicron systems, plus 2 Unknown systems that only have Nomad fighters. I believe around 9 of these are not accessible by Jump Gates (meaning you *have* to find and take unmarked jump holes to get to them). These jump holes can be found by looking at your Nav map, and following some patrol routes that meet up at a single point in space (meaning where 2 or 3 ships' routes converge) or by just making a big circle around the entire star system, focusing inside clouds & debris fields until you turn up a jump hole. Pretty much every system that is linked by a normal Jump Gate is also linked by jump holes that criminals use to keep away from police space. It's not necessary to find these holes in the "normal" sytems like libery or rheinland, unless you *have* to avoid the police & military.