From the picture it looks like either diabase or quartzite (two very different kinds of rock, hard to tell from the pic). If it is diabase it will not polish up as the softer minerals will wear down more than the harder minerals so that the rock will remain pitted no matter how much it is polished. If it is quartzite then it might be possible to polish it a bit, depending on how well recrystalized the grain boundaries are. To tell the difference, use a magnifying glass to look at the rock up close. If there are black or dark mineral flecks between the grains then you probably have diabase. The overall grain texture looks more like quartzite to me but my wife leans toward diabase (yes, we're both geologists).