The A4 Rhombic Dipyramid

In my last Instructable we looked at The A5 Rhombic Pyramid. In this effort we double it, using an A4 sheet, to create The A4 Rhombic Dipyramid. To do so a variation on our standard fold pattern is introduced, based on what we learned from the A5 folds. See https://www.instructables.com/The-DIN-a-Rhombic-Py...

The materials required are the same as with my earlier work - - at a minimum, A4 paper and tape. A straight edge and scoring tool are recommended for making the diagonal folds. Heavyweight paper such as the 120 gsm used here helps to make a sturdier model. And of course, any A or B series papers will work, as would custom sized sheets with 1:√2 proportions. Like my earlier efforts, there is no need for measuring tools or cutting instruments, just simple folds to full sheets of paper!

For our bonus exercise, A3 paper will be used, and straight edge and cutting tool are required.

The first photograph shows our standard fold pattern on the left, and the new variation on the right. Notice that in the original, diagonals run corner to corner and center to center. The new pattern has all of the diagonal folds springing from quarter points along the sides of the sheet. The original pattern has shifted vertically along the long side, one quarter of its length. Otherwise it is unchanged.

We fold as follows:

In half along the long length.

In half along the short length.

Aligning a corner of the sheet with the center point of the opposing long edge. (see photo)

Repeat this fold at each corner. (These diagonal creases terminate at the quarter points along the sides of the sheet)

Fold from end point of diagonal to end point of diagonal, parallel to short side.

Repeat.

Fold diagonal from quarter point of long length to near quarter point of short length.

Repeat at each corner.

Note: Folds from the quarter points parallel to the long length of the sheet are not required.

Prepare your sheet so that the two folds intersecting at the center are valleys, the rest mountain folds.

Squeeze in at center of sides, then fold in corners to find the form. Turn over and tape as shown.

The Dipyramid is complete!

In a previous Instructable, https://www.instructables.com/DIN-A4-Rhombic-Dodec... we made note of the fact that The A4 Rhombic Dipyramid and The A4 Square Dipyramid are geometrically one and the same. (See last two photos)

In one of my earlier efforts we learned how to form a Double Rhombic Pyramid with an integrated hinge using an A4 sheet: https://www.instructables.com/DIN-A4-Double-Rhombi...

This bonus will demonstrate how, by spreading our modified fold pattern across an A3 sheet, we can create a Double Rhombic Dipyramid with an integrated hinge. To achieve this, we do have to bend our rules and make one simple knife cut after finishing the folds. This is to allow for the required freedom of movement. Proceed as follows:

Fold as shown. (Note: the fold shown in the fourth photograph is achieved by aligning the midpoint of the short side of the sheet with the midpoint of the long side, then creasing while maintaining this alignment)

Cut as shown.

Form as shown.

Tape as shown.

An assemblage of six of these units is seen in the video.

Until next time...keep folding your sheets.