  We call a 3-manifold Platonic if it can be decomposed into isometric Platonic
solids. Generalizing an earlier publication by the author and others where this
was done in case of the hyperbolic ideal tetrahedron, we give a census of
hyperbolic Platonic manifolds and all of their Platonic tessellations. For the
octahedral case, we also identify which manifolds are complements of an
augmented knotted trivalent graph and give the corresponding link. A (small
version of) the Platonic census and the related improved algorithms have been
incorporated into SnapPy. The census also comes in Regina format.
  In the appendix, we show that an ideal cubical tessellation can be subdivided
into an ideal geometric triangulation.
