I imagined a "cosmic fitting room", where you would get a direct view right at your own back without mirrors (it would be hard to do that even with mirrors, as you have to use multiple ones, and position them right, and it would still be hard, as you would be in the way).
This is possible in a small hyperspherical universe just big enough to fit you. This kind of thing is mentioned in Rudy Rucker's book, c. p100.
This can be connected to our space by one kind of clear hole; one with two ends; or a wormhole with no gravity and thus no event horizons. (Hence, it would be clear and not black). Or, you can combine them into a simple "space cup" or "foxhole". Basically a black hole with no singularity and no event horizon. (Thus this would also be "clear"). There would be just a curved "end" instead of a point. And you would go around this end, and up the other side, until you exit the hole.
From the outside, it would look like a "lens" making objects on the other side of it a bit smaller. That's because there is more space going through it, and objects become actually "further away" than they are when you look directly at them baround the hole.
Entering it (assuming the hole is positioned so that the floor goes through it too), a black ring would appear before you, like a gateway you are about to cross through. This splits the image of the outside world into a forward and rear image. As you keep walking, the ring gets thicker, and the images begin distorting at the edges where they meet the ring; curling back to make room for it. Soon, the ring expands into darkness to the left and right, with the outside world images completely forward and behind you. Turn left or right; you are looking at your back. However, it is poorly lit, as all the light is coming from the sides (originally back and forth). Look up, you see the floor.
Keep going, then the rear image expands and closes up the darkness, and you are now apparently back in the outside world right where the hole is, and can look straight up at the ceiling; however everything is further away than if you were just standing in that spot. This is the curved end at the center of the hole.
Keep going, and the whole process reverses. The black ring opens back up, and it is just like before. This is the other side of the hole, and the floor we were previously looking "up" to. A shortcut would of course to be to walk in the direction of where you see your back. Then, the distorted images of the outside world will rotate, showing up and down, and then back and forth reversed from where they were before (This is the other side we had just gotten up to), and then up and down reverses, and then the way it was before.
Keep going, the black ring closes up behind you, and you emerge on the other side.
Watching a person walk through; if they just go straight in and then out, you will just see them get smaller looking like they are further than the hole. Two sides of them will become dark. If you watch from the side, the image of them will distort, like it is being seen from a large angle off to the side, until they reach the end, and then appear normal, but small, and then distort again until they come out the other side.
There is an incredible danger in this structure; of intense beams or sheets of radiation forming that could be deadly. If you are looking at your back, and fire rays of light in the direction of the darkness, the light that does not hit your back will keep going around and around in that circular dimension. As more is emitted, it keeps adding to it, to the point where you can get fried. It's basically the same as the blue sheet that forms on the photon sphere of black holes, except that the light is not blueshifted. Enough of it would still be enough. And you could even have invisible light sources such as ultraviolet and shorter, or infrared.
And even if it is visible light, you would never know that the sheet was in there. The light is traveling in a direction where most of it will not come out of the hole. The same holds for Rucker's hypersphere, where the person lights a lantern. And also, the non-gravitational wormhole as well. This space cup is basically a one ended version of the wormhole.
You could even make an interesting prison out of this. The cell would be the end, and the radiation would fill the space inbetween. So you would need no bars; you would just see a smaller person standing in a warped space, with no apparent barrier visible. He would also see no apparent barrier, but if anyone tries to cross it, they would be fried. The only way you could get rid of the radiation is to insert something to absorb it; or perhaps reflect it out.
Probably no way for such a thing to form in space, though, or at least be able to stay that way. Just interesting what would happen with the laws of the universe like that. Hard to imagine the image of the solid world arpund you distorting like that, as well. Might create some sort of dizziness.