The ornament described herein is a tesseract or 3-d representation of a 4-d object.

The ultimate in Geek ornamentation.

I was trying to achieve the look of the one pictured at this link, but was having difficulties with the tools and supplies I had.

Step 1: Tools, Equipment, Supplies and Componants

For the Big outer box, I used an almost cube shaped baseball or trinket display case I bought at a craft supply store.

For the smaller box, I could not find something suitable, so I made one using he corners cut out of a clear rectangular box (cuboid) and clear glued back together.

Other thing the boxes and glue, I used:

One 9v battery clip,
one 110 ohm resistor,
one small on/off switch,
2 lengths of magnet (coil) wire,
3 LEDs (one was a self blinking type)
hot glue (and so a hot glue gun is appropriate also),
a soldering iron and some solder,
some conductive glue (although you can also run the magnet wire along edges and paint    a gold color to hide it)
A compass (no, not the kind that points north, the kind used to draw arcs and circles),
OR a protractor,
The formula for figuring out the length of the "connecting legs"
and a LOT of patience. Of course, if you have worked with hot glue before, you probably
     already have some of that.

The formula is courtesy of BrittLiv and Kelseymh.   It depicts the square root of 3 divided by 2 * (b - a)

Or as explained by Kelseymh:

sqrt(3)
   ------- * (b - a)
   2

Step 2: Preparation - the Small Cube

To prepare for building, we shall need to fashion a small square (since we purchased the larger one, use the formula to determine the dimensions of the smaller one).

We COULD cut out 6 identical square pieces and glue them together, but being a little lazier then that, and finding it much more efficient to do so, I used the corners of the clear plastic cuboid shaped picture frame/display case.   This created it's own set of difficulties, so cut long, and whittle down (if you cut too much off, you can't go back).

Each corner then, had 3 of the needed 6 sides. Placing them together and gluing with Duco cement was a snap.   I then used some masking tape to mask off most of the sides leaving a .125 inch ( 3.175 mm) edge exposed. I then pained on my conductive glue. After that hardened, I attached a wire (magnet wire) to one corner (this was going to be a ground wire). Then I pained over the black conductive glue with gold leaf coating. After dry, I removed the tape.

Make sure when using magnet wire that you remove the "coating" over the wire at the points where you wish to attach or solder them to have conduction.   Various ways there are to remove this, from solvents to scraping. I prefer using 300 grit sandpaper EXCEPT for very thin wire.

Step 3: Fashioning and Adding the "legs"

From the remainder of the clear plastic picture frame we used a few corners of for the small square, I also cut out some connecting legs to a bit longer then the specified calculated lengths (formula).

This gives me something to work with, in case I accidentally melted or dissolved a small portion of one of the legs (whether you choose to attach them with heat, or with hot glue, or with Duco cement).

Finding the proper angle is a bit tricky though. I used a compass to find the angle from each direction. It is not an exact science here as you will be prone to "move" the piece a few times before it is set. Once you have four of them on the one "end" attached, check to see if it fits in the cube. Then, once you have that working, attach the other four legs accordingly.

Step 4: Placement of the LED's and Finishing Up

Now would be a great time to wire up the battery clip, switch, resistor, and three LEDs. Use the magnet wire to wire the LEDs as in the schematic. I cut a small hole in the bottom of the small cube for the flashing LED, and the others put on opposing corners.

Run the magnet wire along the edges, another coat of Gold leaf should help hide them well.

I also placed a notch in the one corner of the large square, for the magnet wires to exit.

For a little added panache, one could, before making final solders to the battery clip, slip a section of shrink tubing over the wires that exit the cube, and heat the tubing so it seals and protect the magnet wire.