This setup refers to the first structure
First up : The Mirrors. Obviously face to face offers the best continuity of reflection (though as of yet, Anim8or cannot "truly" reflect indefinitely ). In this example I arranged six planes into a cube. Making individual sides instead of just a cube allowed me to have individual textures for each side. Make the first face and then subdivide it in point mode using Edit/Subdivide a few times. This step is important especially if you wish to use modifiers (fun-house mirrors for example). Next assign textures and attributes and copy and paste 5 more so ya don't have to keep typing in the attributes for each face. Arrange into a cube and your done.
Second : The Frame. Well...I'm sure your capable of building one. The frame in this example is simple a re-worked cube. Just make sure some or all of the frame is within the cube for the obvious reason that there needs to be something to reflect. Alternatively place an object within the cubes confines, or at least have the mirrors textured.
Lastly : Modifiers. Twist, bend and curve your structure into shape. Careful how you do this too much warping can be a detriment to the results. You really have to experiment for what works best.
Now : Scene Mode. Obviously the camera is inside the cube so the angle of arrangement is up to you. FOV is also very important to the renders I've done. Generally 90 degrees is my comman setup but I have used 120 and 135. As for lighting typically only light up 3 adjacent faces ie. no opposing lights as I generally get white wash renders. Set to render go watch a movie or two and it should be done.
Attributes : class - glossyreflector ; Kr - 0.85
Amibient : 0.5 RGB 255 255 255
Diffuse : 1 RGB 255 255 255
Specular : 0.75 RGB 255 255 255
Emmisive : 2 RGB 255 255 255
Rough : 100000
Brilliance : 10
Trans: 0.9
Number of rays used in last example : 587,839,617
Above all, Thanks for your critiques and now I've given away my secrets how about some examples by yourselves? That would be cool.
No prizes for this but guess which render used 4 Convex mirrors.
Render 5 is a Dodecahedron