Löbell manifolds revised

The first example of a closed orientable hyperbolic $3$-manifold was constructed by F. Löbell in 1931. It was an affirmative answer to the Köbe question on the existence of hyperbolic $3$-forms. In the present paper we give a short survey of some related results and obtain a simple analytic formula for the volume of the Löbell manifold as well as for volumes of Humbert manifolds.