This is actually the first model I came up with. It was probably in 2014 or 2015?
I use red dashed lines to represent valley folds, and green dashed/dotted lines to represent mountain folds.
In other words: start with a piece of square paper, white side up.
Valley fold in half on the vertical and horizontal lines. Mountain fold in half along the diagonals. In each case, crease, and then unfold.
In real life, of course, you'll want to use paper that's actually SQUARE....
Turn square so a point is up. Valley fold left and right points into middle along vertical lines; crease.
Then, fold entire model in half along horizonal center line (where a "3" is marked in the illustration).
Turn folded model so point is up and longer flat edge is down ("house shape").
Step 2 is left & right points folded in; step 3 is folding entire thing in half.
Fold as shown in illustration; position the fold so its lowest end is roughly 1/3 of the way from the center vertical to the outside edge. (You can play around with exactly where it is to change the final shell shape.)
Crease fold, then unfold. The next steps may be easier if you both valley fold and then mountain fold along the same crease.
Repeat for both left and right lower corners.
Left side is how model looks at the start of this step. Right side shows this step in progress.
Inside reverse fold lower corners into center of model, as shown.
With lower corners folded into center, shape should look as shown at right. Make sure all creases lie correctly. Check in center of model to make sure that middle points of the right and left sides (which you've just inside-reverse folded) are actually lying flat and the points are at the center.
I'll call the right-angle triangles created by the Step 5 inside-reverse folds (on the right and left sides of the main diamond shape) flares.
Then, valley fold as shown to create a horizontal crease somewhat below the lower horizontal edge of the left and right flares. Crease hard, then unfold. Later steps may be easier if you also mountain fold & crease/unfold along the same line.
Shape is how model looks at the start of step 6. Red fold line is fold described by this step.
Sink fold the lowest point up into the center of the model, using the creases/lines you created at the end of Step 6.
The illustration at right shows (very, very roughly) what a bottom view of this looks like, if you open out the model to sink the bottom point. (I find that's the easiest way do this. Maybe the only way? I don't know.)
Once the sink fold is done, make sure all layers and creases line up correctly (inside & outside, especially including inside corner points where they are folded into center) and then crease everything firmly.
Image at right shows the model shape at the start of this step.
Carefully reverse the sink fold from step 7. Then, carefully reverse the inside-reverse folds for the left and right "flares" (lower corners).
At the end of this, the shape should be back to the 5-sided "house" shape it had at the start of step 4. Now, though, it will have pre-creases for all these ensuing steps.
Why do it this way? Because it's much easier to set those creases now (before the following steps), then just re-follow them at the end.
This is how model looks at the start of step 8. Then, you'll undo all your hard work thus far....
Valley fold the lower-right diagonal crease so it lies on top of the vertical center line, as shown. Crease, then unfold. Repeat on left side.
This bisects the left and right halves of the central "diamond" shape, so the new folds almost form rays from the bottom center to the top right and left edges.
Later steps may be easier if you either (1) mountain fold along the same lines, crease, and unfold; or (2) only valley-fold the top layer into the middle, then flip model and repeat with (new) top layer & (new) center. Second option is especially useful if you are using thicker paper.
Left side (ignore folded-over flap from right) is how model looks at start of step 9. Right side shows step 9 in progress.
Much like you folded step 9, fold the lower right diagonal crease up so that it aligns with the new right crease formed in step 9. Flatten and unfold; now you have a new "ray" splitting the rightmost segment from step 9 into two segments.
Do the same thing with the right diagonal crease formed in step 9, aligned to lay over the vertical centerline (the new crease here splits the upper right segment formed in step 9). Crease & unfold.
Repeat on the upper left side.
Again, you can either fold both front and back layers together (esp. for thinner paper) or fold front layers alone, then flip model and fold back layers alone.
Experiment with both mountain- and valley-folding along each crease (so the fold lines are visible but ultimately lie flat) vs. leaving them as mountain/valley folds. These give different effects to finished shell.
Inside-reverse fold the right and left lower corners into the center of the model (again), along same lines/folds used in step 5.
Check to make sure center layers align correctly, especially center points of right and left sections (which should be all the way into the middle).
Sink fold lower point up into model along fold lines created before. Again, carefully check that everything is aligning correctly (the new folds from steps 9 & 10 can complicate things) before creasing to set folds.
Shape shows model at end of step 11; green lines are folds going into step 12. Left and right corners should be proportionate; they aren't here b/c the drawing is skewed.
Mountain fold top corner into center along line shown in step 11 illustration; repeat behind.
Mountain fold left and right points into center along lines shown in step 11 illustration; repeat behind.
Because of the way the lower right and left corners lie inside the model, the left and right points (once folded inside) can actually be "tucked" inside the paper layers already inside. Hard to describe, pretty easy to see when it's in front of you, and not essential regardless.
If desired, add an extra inside-reverse fold to lower right and left "flares" to reshape, as illustrated at right. Left side of illustration shows original flare shape and approximate fold lines for inside-reverse fold. Right side shows result after reshaping.
Shape top & sides (see mountain fold lines from step 11 illustration). Optionally, reshape right and left "flares" with inside-reverse folds along lines shown at left, to create shape shown at right.
Model holds its shape better if it's either weighted or glued in the very middle or "hinge" of shell, especially if using heavier paper.
Experiment with how much you flatten (or don't flatten) the "ray" folds. Top and bottom shell halves can match or oppose each other in mountain/valley folds for different effects.
You can also experiment with the angles/placement of mountain folds shown in step 11 drawing (final reshaping of points).