Today we add a new Basic Building Block to our tool kit, The A3 Elongated Octahedron.*

In order for this model to remain at the same scale as our previous "blocks" - the A4 Dipyramid and the A4 Parallelepiped - this shape is formed from full sheets of DIN A3 paper, twice the size of A4. A similar fold pattern is required.

*https://en.wikipedia.org/wiki/Elongated_octahedron

Supplies

As with our previous models, in addition to the A3 paper, the only tools and materials required are tape, a straight edge, and a scoring tool.

Step 1: The Fold Pattern

As we see from the first photo, the finished fold pattern resembles our standard A4 pattern (see my previous Instructable: https://www.instructables.com/id/UnFolding-the-Mys.... The pattern is extended across the larger A3 sheet when rotated 90 degrees, from Landscape (A4) to Portrait (A3) orientation.

In this case the orthogonal folds divide the A3 sheet into eight equal parts along the long length, and four equal parts along the short length.

Begin the diagonal folds by aligning diagonally opposite corners, bottom right to top left, then bottom left to top right, to make the first two folds through the center of the sheet. Then fold the remaining diagonals as shown.

Scoring the diagonals before attempting the fold is recommended.

Step 2: Forming the Figure

The photos illustrate how to form the Elongated Octahedron. The two triangular faces at either end of our octahedron are formed much like we do the Dipyramid (again, see my previous Instructables). Then, the four trapezoidal faces of our figure can be found.

Apply tape to the interior seam at either end, then as shown.

The finished form can be seen as the augmentation of 2 dipyramids, sharing a common edge, with 2 tetrahedrons filling in the gaps, top and bottom.

Step 3: A Kinematic Chain

For our kinematic chain we will link A3 Elongated Octahedra with A4 Dipyramids. Four of each of these are required for this model.

Begin by hinging together one Elongated Octahedron and one Dipyramid, as shown. When hinging, carefully align edges and be sure to apply tape to both sides at each hinge. Repeat to create a total of four linked pairs.

Hinge the pairs together, as shown.

You're done!

For more detailed instructions on hinging, see my previous Instructable:

https://www.instructables.com/id/Mysteries-of-the-...

For more on the special nature of DIN A proportions, see:

https://www.instructables.com/id/Dipyramids-UnMask...

Be safe, and have fun making your own discoveries!