One of the special modes of 3D printing is Vase mode, which reduces the structure to a single extrusion line, spiralized around the outer perimeter.
The most simple vase would be a cylindrical spiral, with each rotation of the spiral going up 1 layer height. By adding variance in the spiral, you can come up with some pretty cool shapes. They are popular for demoing a printer, due to the continous printing nature and the continous motion of the z-axis, it is easy to see progress in a short amount of time, and large prints run much much faster.
Here are some of the vases I have printed.