Distance-creating "lens"?

On another recent question I noted that it’s theoretically possible to take “short-range” pictures that have the perspective as if they were taken at a distance, by means of a system of mirrors:

To be fair, a “lens” could in principle create distance greater than any external dimension of the lens if it’s actually a system of mirrors and lenses by bouncing light rays back and forth multiple times

with another user noting:

But only if the first refractive surface (or curved reflective surface), as opposed to flat reflective surfaces, is placed at the other end of all of those mirrors

Is there any commercially-available lens+mirror assembly to achieve such an effect? If not, are there any write-ups/tutorials on assembling something practical?

Here’s an awful ASCII-art diagram of a possible design (shown as cross-section):


where horizontal and vertical strokes indicate path of light inside the enclosure and diagonal ones are mirrors at 45-degree angles, with light entering from the top-left and exiting (to refractive lens stage) on the right. As drawn, it should add an effective 5x the length of the “lens” to the distance to the subject; to be of practical benefit it probably needs to be fairly long and/or have a few more loops but I didn’t want the ASCII art to get any more unwieldy.