It is not all that fruitless.
A ribbon is clearly two-dimensional, having length and width, but it is used to substitute a one-dimensional string. In practice, these are three-dimensional things, with one free dimension - length. For this, one might use the word 'latrid' (1d-ish).
A fence is essentially a replacement for a line on the ground. The height of the fence is not dependentant on the area it encloses, but rather the effort of the closure.
It is a line around an area, with height. The pan-dimensional thing is that a fence is a bound of surface (area), with height. If you think the height is part of the figure then you would count it as N-1 dimensional.
However, it is best to regard the ground as N-1 dimensions, and any dividing space as N-2. This is how it appears on maps. Since we already understand the idiom that the real world is map + height, the use of the map notion serves to better visualise it.
For a fence, it really does not matter how long it is, for the purpose of visualising it. The height and width of it is more to do with dealing with stopping crossings, while only the portion of it on the map says where the crossings are not permitted.
A fence, then is rather like a ribbon, in that given a cross section, it can be usefully repeated in just one dimension, and therefore is a latrid thing.
The dream you dream alone is only a dream
the dream we dream together is reality.