  We consider Meissner polyhedra in $\mathbb{R}^3$. These are constant width
bodies whose boundaries consist of pieces of spheres and spindle tori. We
define these shapes by taking appropriate intersections of congruent balls and
show that they are dense within the space of constant width bodies in the
Hausdorff topology. This density assertion was essentially proved by Sallee.
However, we offer a modern viewpoint taking into consideration the recent
progress in understanding ball polyhedra and in constructing constant width
bodies based on these shapes.
