Why is There No South Star?

I think most of us are familiar with the North Star (officially known as Polaris).  It's a relatively bright star in the northern sky, pointing north and not moving from its position in the sky.  It sits directly above the North Pole, or Earth's axis point.  It's commonly mistaken as the brightest star in the night sky.  It's a bright star, but there are several brighter stars in the sky.

So why is there no South Star?  Actually, there is.  It's Sigma Octantis.  We don't hear much about it because it's much dimmer than the North Star (see image below).  It's about 25 times dimmer, so it doesn't stick out nearly as much as the North Star.  Like the North Star, the South Star sits directly above the South Pole (or close to it) and doesn't move much from its position in the sky.