Hi!
Had the shapeoko 5 4x4 for about 2 years and finally found a project I want to do… but its just from a video from FB…
It’s an awesome pyramid box that has a well designed opening system… I will try to upload 2 pics and add a link to fb…
Would anybody more experienced than me be so kind as to have a go at making the files for this please?
Lot of math/engineering goes into figuring out where to put the holes & slots to make it work.
I got the first 2 levels done… 
I went with 8 x 8 x 6.75 tall. (9 layers of 3/4")
It’s pretty straight-forward when one considers that the base shape is “just” a cube sliced off at a given set of angles.
If not using 3D modeling, then the angle must conform to that of an available V tool, so 45 or 30 degrees (half 90 or 60 degrees) — doing a bit of modeling, we can get a quick 3D preview to see which would be best:
Since the former seems a bit squat, and the latter seems to better match the proportions of the image, we will use 30 degrees.
The next consideration is what size tool will be used.
Amana sells:
which has a cutting depth potential of 59/64th inches.
59 / 64 inches = 2.3415625 centimeters
so rounding that down to 2.25cm seems reasonable, and with 9 layers we arrive at overall dimensions of:
Spacing out 9 lines:
Duplicate everything to a reference layer:
and hide it
Then select everything and use Trim Vectors to make alternating sets of layers:
Arriving at:
Select all and Join Vectors
Yes
Delete the open geometry:
then draw in the alternating layers with the Polyline tool:
It is then necessary to create each layer and add insets to define the pockets and lay those out to create the structure necessary for the hinges and magnets.
Draw a pair of squares which match the sizes of each layer:
Probably it will be easiest to have each layer on its own layer, stacked:
First we set up some toolpaths to verify that we have our dimensions right and things have the correct appearance:
(the bottom will not have a pocket, since it is not accessible, and needs to have solid structure to it to support everything above it)
The second layer is divided into fourths with a central square pillar rotated 45 degrees:
This may then be inset:
Note that at one corner additional structure will be needed to allow for a hinge post for rotation — rather than the thicker edge, notching this corner seems a better appearance, which is easily done by duplicating and flipping and getting the intersection:
OK
A post/hinge will be necessary at this corner — this is easily positioned by drawing a square:
and drawing a circle centered on that corner:
and adjusting the position until it is well-placed in this area:
It will be necessary to have rotated copies at each corner:
repeat for each remaining corner:
The four circles should be copied to the bottom layer:
Similarly, there should probably be a central post placed in a hole on the bottom layer, up through the diagonal block and up to the fourth layer:
Apparently this is a two-sided job for some layers and there should be pins placed so as to have one layer rotating open up the next layer down…
The third layer up looks to be solid, but as noted will be a two-sided part with some locator pins to make the second layer open.
Adding the geometry for this, it becomes apparent why certain edges were thicker:
so we duplicate and rotate and do Boolean Intersection again:
I am pretty sure that for the rotation to work it will be necessary for the hinge and pin to be along the same axis w/in the region of the base, which the above additional notch facilitates.
Duplicating them into the corners we get:
(which as noted will need to be located on the bottom)
Looking at the mechanism again, it may be that these will need to be slots — which would explain the added thickness — may have to model this in full in 3D and add an animation component to verify that, or perhaps a cardboard prototype is in order…
The fourth layer is a replica of the second, just smaller along XY:
and it will also need a central diamond and so forth:
and the same sort of notching (and possibly wider wall, although one wonders if the precision of CNC would allow the slots to be shallower, and perhaps that they could be closer to the pockets if they pockets were rounded along their edges…)
Anyway, the above should get folks started, and at least allow cutting some prototype parts to test fit and mechanism and work out whether the slot and so forth are needed.
That’s pretty much what I did…
I assumed 3/4" stock, and 8 x 8". Worked out to 30.65°
At 6 3/4" tall, 30° would be 7.794 x 7.794". 8" allows for a little slip clearance between layers, and I think once you sand down the outside it will all even out. In other words, “close enough for all practical purposes.” **
I also added clearance (0.010") between the parts, 0.135" holes & slots for 1/8" dowels / pivots.
You also have to work out where the hinge & slot need to be
** …which was defined by my HS math teacher thusly: If you line up all the boys on one side of the room, and all the girls on the other side, and at even intervals half the distance between them, in theory they would never meet. They would however, become close enough for all practical purposes. 
Nice visual of the rotation! Thanks!
I believe that that should be the last bit of information anyone would need to take the above and finish this up.
For review, here is my initial/unfinished version of the file as I left it:
pyramid_box_v8.c2d (92 KB)
@Swayzxpress Let us know how it works out!
Awesome guidance thanks! Really appe-reciate the detailed break downs. This will be my first project so can’t wait to learn some stuff and see something materialise. Looking forward to showing the finished product one day. Might stop the wife giving off about it 
Will be happy to see someone beat me to it though!
You guys are awesome for walking us all through that. Thank you!
Thanks for showing us this project!
