Here is a simple do-it-your self experiment. This a fun way to look at math and light and multiplication and contemplate dimensions and so forth.

You will need:

6 squares of mirror - if these are standard decorative mirror tiles (which are bought precut in box) then you will not need a glass-cutter which requires some skill to use.

Duct tape and aquarium cement.

A true lead-glass prism (that will cast rainbows), it should have a large primary flat facet. Most are round, but look for one that disk shaped with a primary flat facet. Any good prism will work.

A new single edge razor blade.

A pencil with an eraser and some baking soda.

Maybe some real clear glass glue to the prism on.

Some sunshine to ignite to the prism.

First take 4 of the tiles, clean them as good as possible and make four walls of them on a flat surface. Tape the edges at 2 or 3 points with removable tape tabs (as shown). Take 2 panes like a closed book where the tape is a hinge, tape firmly on the edge and open like a book. Stand the 2 like books open and on end so they make a square and tape the rest of the edges. Just having the tabs is for adjustment.

Sight the mirror so the reflecting tunnels are strait and not twisty. Also check to see if they go strait and don't slope up and down. If it is not possible to make them perfect, try to make them even out somehow. Adjust the tape tabs to make corrections.

After you are satisfied, either tape it up or carefully apply silicon aquarium cement in the edge. Glue or tape the walls in such a way as to prevent any stress that will cause the edges to grinding and creating tiny splinters. Doing this will make a more durable box, but tape will work for a quick experiment.

You will be able to nudge some of the edges slightly inside of the other while leaving the tabs on. The glue will keep them in that position. This will also create a tiny edge to keep the top and bottom lids from falling in.

If you don't want to see the light on the edges, then use black silicon glue, or cover it with tape afterwards.

This will all become explained when you start putting it together.

Later when the top and bottom go on use the same method. You may want to put the top and bottom on in two separate steps if you have any difficulty with the top and the bottom wanting to fall inside because of being the same size as the opening of the box.

Later when everything else is done this little gap will be where the glue is put.

When the glue has dried, then take the tape off.

(Be careful to not squeeze glue through to the inside of the box.) Tape can be used but it is better to much glue. In all the adjusting You will be able to find a position that works and doesn't squeak or scrape. Pull the tape tabs off if you need to make an adjustment.

Now the hard part - estimate the distance your eyes are apart to create a hole in the mirror. On the gray backside draw (a small area) on one of the 2 remaining of the 6 mirror squares to create a view inside.

The area should be reasonably small which will make it easier.

Very carefully and slowly firmly scrape the gray mirror backing off.

You should use a safer tool like a scraper tool to hold the razor and a brand new blade.

If you don't then you will have press HARD at a maximum slope to cut into it. (about 45 degrees). Be sure to pull and not push the razor BECAUSE the razor is likely to flip back because you need push hard.

EXPECT the extremely sharp brand new blade to flip back - it will and does.

If you hold it as shown it is reasonably safe.

Also - remember that the mirror will crack if you push hard on it. It should be on a very sturdy flat surface.

The more you get off with a new sharp razor blade the easier it will be.

Next you will find that there is a copper film beneath the gray surface. It is electroplated on and is difficult to remove unless you are firm and precise. You will not be able to get it all off. So then take some baking soda and use it to grind off the rest using the pencil eraser.

Actually the easiest way to get it off is to dip the pencil into a car battery and carefully get a drop (or less) of the acid and put it exactly on the place you are trying to polish. If you do this, remove the baking soda first. Wait a little while and the acid will corrode or weaken the copper film a little bit - then wash it off and try again with the eraser and baking soda. It will polish off either way.

Then do the same with the other pane of mirror, make the hole the size of the prism and glue the facet on with a tiny dot of crystal clear epoxy. A tiny amount of glue will not obstruct the transparency of the prism. It could be glued on the inside or outside of the box. Or it could be attached over the hole by some other clever method.

The box can be covered with decorative contact paper or something.

Point the prism towards the sunshine and prismatic beams of light will dazzle your mind!