Actually, it's even more interesting than that - in the House of Commons in London, there are two facing sets of seats, and a carpeted aisle between them (like our House of Representatives, if the two parties were looking at each other rather than at the Speaker).
There is a line in the carpet in front of each party's benches. Members of Parliament are forbidden to walk any farther forwards towards the other party than their line. That is because a person standing on that line cannot quite reach the other side with a drawn sword to skewer their counterparts. Members had to 'toe the line' or they would be ejected.