Solid tori are important elementary type of 3-manifolds. Also called orientable genus one handlebodies and can be fibered -in the sense of Seifert- by longitudinal circles, and in many different ways.
Among three dimensional technologeeks, they are customed to see a solid torus that can be fibered as the , the twisted interval bundle over the Möbius strip. In constrast is the genus one non orientable handlebody: the solid Klein bottle. Isn’t difficult to prove that they are the only two -bundles over