I was going to make a vaguely snide comment about difficulty in routing and managing services (air, water, power, data, &c.), but the more I look at the model, the less firmly I'm convinced that there is an intractable topological problem involved.
I'm still going to go with calling it the Villa Straylight, though.
That was more or less what I had in mind. On the other hand, it might be more cost-efficient in general to design the cylinders to connect endwise and form a hexagon; it'd increase travel time for the station's inhabitants, but reduce the need for unique construction tooling -- instead of seven types of cylinders, each of whose interconnections are placed differently from those of all the others, you build one type of cylinder and one type of connector, then fit out each unit according to the purpose it serves in a given station design. You can also enable more complex topologies simply by developing more complex connectors, whereas what I shall please myself by calling the "eccentric" design under discussion doesn't scale nearly as well.
That scales better than the eccentric design, but not as well as separate connectors.
Suppose, for example, you want to be able to assemble, from the same components, a flat-hexagon station, and an "asterisk" station like what you'd get if you drew radii from each vertex of a hexagon and then took the hexagon away -- a configuration which might be very useful, for example, as a "transfer point"; if the inter-segment connectors are adaptable to whatever standard governs spacecraft airlocks, then you can dock at least six spacecraft at once and interchange cargo among any or all of them. If you add a seventh "socket" to your central connector, normal to the plane of the other six, then you can tie your "transfer point" to a larger station, too, and assemble a larger structure, as for example might be very useful at a nearby Lagrange point, as a way station for ships inbound to and outbound from the Earth-Moon system.
(On the other hand, perhaps I simply spent too much time playing with Tinkertoy as a child.)
It was great: whether by design or luck, the poles you had to climb got more and more horizontal as you got higher from the ground, then they became inverted in a way that made the topmost part easy and safer. The bottom then was a test: if you failed you had not far to fall, if you succeeded you would likely be ok to the top.
Easy to go everywhere from everywhere.