  We describe the deformation space of a solid torus with boundary modelled on
convex ideal hyperbolic polyhedra. This deformation space is given by natural
Gauss--Bonnet type inequalities on the dihedral angles. The result extends to
solid tori with an arbitrary conical singularity along the core. Our method is
to decompose the torus into tetrahedra and maximize a volume functional.

Geometric Topology