We examine a particular kind of six-dimensional Cremonian universe featuring one dimension of space, three dimensions of time and other two dimensions that can*not* be ranked as either time or space. One of these two, generated by a one-parametric aggregate of (straight-)lines lying on a quadratic cone, is more similar to the spatial dimension. The other, represented by a singly-parametrical set of singular space quartic curves situated on a proper ruled quadric surface, bears more resemblance to time. Yet, the two dimensions differ profoundly from both time and space because, although being macroscopic, they are *not* accessible to (detectable by) *every* Cremonian observer. This toy-model thus demonstrates that there might exist extra-dimensions that need not necessarily be compactified to remain unobservable.