All of the links I've seen are to sites where it is implicitly or explicitly assumed that the dirigible is a homogeneous sphere. This approach does have some merits - any failure has to originate at some point, and if the sphere is absolutely uniform then there is no obvious point of first failure; and in the analogous situation of deep sea exploration spherical construction has been shown to have its uses. However, in practice no material construction is ever completely uniform, and even if one was, until the dirigible was aloft there would be a difference between those points which were in contact with the ground or supporting structures, and those which were not.
It seems to me that a much better approach would be to have something which is approximately spherical, but which is supported internally by a complex system of ribs and buttresses, akin to what can be found in a gothic cathedral.
For a starting point, take a look at e.g. http://www.cutoutfoldup.com/905-spherical-model---cube.php.
Imagine this structure scaled up and manufactured to extremely high precision using the strongest available materials, and covered by a thin film so that the interior is completely enclosed. What you'd have is essentially a sphere which is very thick at certain points (i.e where the ribs are) but very thin at others. The ribs would be able to withstand enormous pressures. The other points - not so much. As it stands, it would fail at one of the non-ribbed points. So, not a great advance. But now imagine that the material of the faces is quite strongly curved; that each face is a portion of a sphere which is much smaller and therefore more strongly curved than the overall sphere. These smaller spherical segments should be able to withstand a much larger external pressure than a large sphere of the same thickness.
Now imagine each of these bubbles is itself ribbed, with the facets between the ribs occupied by still smaller ribs and bubbles. The construction is effectively fractal, with the repetition at smaller scales occurring as often as is required. The very smallest bubbles would be very highly curved, and therefore very strong. The external pressure exerted on them would be directed to small ribs, which would in turn be directed to larger ribs, and so on. I don't know of any attempts that have been made to construct a vacuum dirigible along those lines, but I don't see why it shouldn't work.
EDIT: If we understand that any vacuum achievable on Earth using a mechanical pump is in fact just a partial vacuum, and we therefore use the word "vacuum" as an abbreviation for "partial vacuum", it follows that "vacuum dirigible" and "lifting gas dirigible" are not mutually exclusive terms. It should be possible to construct a dirigible containing hydrogen or helium at significantly reduced pressure, instead of the slight overpressure that is normal. The rigidity would then have to come from the structural rigidity of the shell instead of from the internal pressure.
The big advantage, in the case of a reduced pressure helium dirigible, is that under normal circumstances the loss of helium to the atmosphere should be negligible, unlike a normal balloon where losses are substantial and have to be continuously replenished. The major gas seepages would be from the higher pressure exterior to the lower pressure interior, and any potentially escaping helium would be in effect swimming against that current. It would also be seeping through a rigid material which is likely to be more impervious to the flow than a more flexible material would be. This advantage will become increasingly significant as the price of increasingly rare helium continues to skyrocket.
Not that it should be necessary to employ reduced-pressure helium, it's just that doing so would make construction easier by decreasing the pressure difference between interior and exterior to something more easily manageable. But I'm fairly sure that with an intelligently designed shell it would be possible to create a working dirigible even with the interior close to being a hard vacuum. The article cited by RedGrittyBrick in his answer states "the best materials fall short of achieving our aim by a factor of just over 2", and I am sure that a better structural design would result in MUCH more than double the rigidity of a simple homogeneous sphere for the same mass of material. Supercat's anecdote, below, helps to illustrate that.