The story is set beneath Buenos Aires, deep within its labyrinthine subway system, and centers on a train containing 30 riders that has mysteriously disappeared. The subway officials are greatly troubled and so call in topographer Daniel Pratt to help them find it. Unfortunately, the tunnel system is so vast and complex, that Pratt must find his mentor Hugo Mistein for help. Unfortunately, he too has disappeared. Fortunately, he left the system plans behind and as Daniel studies them, he comes to the awful realization that the train, which can be heard but not seen, has somehow become trapped in a fourth dimension. His findings attract the attention of local bureaucrats who are too rigid and pragmatic to accept Pratt's outlandish theory.
In the bowels of a busy subway system, a train and its forty or so passengers mysteriously vanish one morning, seemingly into thin air. The "missing" train doesn't show up on any of its regular stops, and searches for it yield nothing. Yet it can still be heard at certain times, and the system's intricately worked out system of tracks and signals continues to function as if the train were still running.
The system engineer is called in to check things out, but declines, instead dispatching Daniel, a mathematically minded young professor, in his place. The inquisitive Daniel's first stop is the home of the mysterious Dr. Mistein, who is nowhere to be found, but has the plans for the subway system's layout stashed in his house.
Having formulated a completely outrageous solution to the problem of the missing subway train, Daniel calls a meeting with the subway's superiors. His idea is that the subway system, with its countless add-ons over the years, has become so incredibly labyrinthine a gigantic moebius strip was unwittingly created which the missing train is now trapped on.