CREATING A RECEDING RECTANGLE IN AFTER EFFECTS

My apologies, but I'm kind of a left brained guy and sometimes it's hard to wrap my mind around right brain spatial problems that others find laughably easy.
I'm interested in creating this simple box with four walls through which one could view a video at the far end.  I don't need all the little videos on the side, I am just unsure how to create that simple box.
Would I extrude that in 3d somehow?  Can I construct it all at once rather than aligning one wall at a time?  I'm not too good with parallax and vanishing points yet.
What basic workflows do I need to master to create this simple box in 3D?
Thanks so much!  Rocket science to me right now.
Here is the underlying video from which it was derived; it was constructed in another program, but I'm certain this is very straightforward in AE.
https://www.youtube.com/watch?v=qvP6mFokVCETh
Thanks!   Matt Dubuque

Position the anchor points is purely mathematical. Think of a cube with all of the anchor points for each layer exactly in the center of the cube. If the sides were 400 pixels by 400 pixels then 1/2 of the width or height would be 200. Offset the anchor point by 200 pixels in Z and you've moved all of the layers back by 1/2 the width of the layer. Since rotation always happens around the anchor point when you rotate the in increments of 90º they will always end up with aligned edges.
Now to the problem of your edge seams. First of all, work with even pixel values for the size of your layers. 200 X 200 works, 205 X 205 or 300 X 145 won't work as well. This is because AE does sub pixel positioning and the edges at half pixel values will be interpreted with different values than edges at whole pixel values.
The second problem is that any time there's any angle to a line or edge the edge must be interpreted to fix aliasing (jaggy edges) that are caused when you try to draw a diagonal line on a checkerboard. It is called anti-aliasing. This gives you different pixel values at the edge with the image is at an angle. After Effects makes it's transparency calculations using straight alphas. In most cases this is by far the best option. When it comes to matching up edges of these 3D planes it isn't the best. It would be better to add the alpha values together rather than use a straight calculation which combines the values.
Fortunately AE has a blend mode called Alpha Add. It only effects the alpha channels are calculated.  Changing the blend mode to Alpha Add eliminates the problem until you start adding lights to your scene.
As soon as you start adding lights to the scene you run into additional problems calculating alpha edge values. There are some workarounds to eliminate light leaks in these situations that involve scaling the layers slightly that are nearest the camera so that the problem is hidden. In spite of what your wife says trying to be perfect in every frame isn't a very good way to make a living in the visual effects business. You have to be able to make your scene look right with the least amount of effort so you can move on the the next of the thousands of frames it takes to complete a project. That is the biggest challenge faced by anyone working with AE.
Unfortunately, unless you use ray traced rendering to extrude a box in AE you cannot fix the problem completely, but by carefully designing your animation to hide these problems you can make things look perfect without being so. Take these two cubes with a point light set in the center. The one on the left is perfect but looks wrong, the one on the left has the back left wall moved 1 pixel to the right and the right front wall is scaled 101% in X to hide the seams. If I needed to spin the cube and add motion blur I would need to pre-compose the spinning cube and add CC Force Motion blur to the scene to hide the seams. It's prety easy to see which version of the spinning cube works better.
I hope this long winded explanation helps. Take a look at his image. It shows two solids separated by 2 pixels in the center. The Alpha levels of the pixels that are going to match up are shown. The panel on the left shows the edges matching with the blend mode set to Alpha Add. The image on the right shows the blend mode set to normal. The differing shades of blue are caused by combining rather than adding the alpha values of those pixels.

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