Sturdy Edge Units

As their name suggests, Sturdy Edge Units are very sturdy. The additional creases make this unit much stronger than Penultimate Units, but the range of shapes they can form is much more limited. Example models include my Icosahedron and Rhombicuboctahedron.

This unit was independently invented by several people, including Dirk Eisner, Francis Ow, Michał Kosmulski, and Tomoko Fuse.

Base Unit

Materials: Only paper is needed. Start with a sheet of letter-sized paper. Fold one corner diagonally to meet the opposite edge, then cut off the excess to leave the largest possible square. Divide this square into 4 smaller squares; each unit uses one.

Step 1. Fold the paper into quarters in a wavelike pattern, as shown.

Crease pattern of a small square of paper folded into quarters in a wavelike (accordion) pattern, forming a flat strip with alternating mountain and valley folds

Step 2. Unfold the middle crease, but keep the two sides folded. Place the paper vertically with the flaps on top, as shown.

Folded paper placed vertically with the middle crease unfolded and the two side flaps still folded, flaps facing up

Step 3. Fold the inner edge of the left flap to meet the left edge, and unfold.

Middle edge of the left flap folded over to meet the left edge, then unfolded, leaving a new crease

Step 4. Fold the top right triangle to meet the new crease created in Step 3, and unfold.

Top right triangle folded over to meet the crease made in Step 3, then unfolded, leaving a diagonal crease

Step 5. Tuck the new triangle inside the paper with an inside reverse fold. This creates the pocket of the unit.

New triangle tucked inward with an inside reverse fold, forming the diagonal-edged pocket of the unit

Step 6. Repeat Steps 3-5 for the other side.

Steps 3 to 5 repeated on the other side, so the paper now has a tucked pocket on both the left and right

Step 7. Valley fold the entire left half on top of the right.

Entire left half valley-folded over the right half, producing a narrower layered shape

Step 8. Valley fold the top right flap as shown. The new diagonal crease should coincide with the diagonal pocket edge created in Step 5.

Top right flap valley-folded so the new diagonal crease lines up with the diagonal pocket edge from Step 5

Step 9. Valley fold the small rectangular flap on the left towards the center. The new crease should coincide with the left edge of the piece.

Small rectangle on the left valley-folded toward the center, with the new crease lying along the left edge of the piece

Step 10. Repeat Steps 8-9 for the other side.

Steps 8 and 9 repeated on the other side, giving a symmetric folded shape

Step 11. Slightly relax the creases created in Steps 7-10 to finish!

Finished Sturdy Edge Unit with the creases from Steps 7 to 10 slightly relaxed so it opens a little, showing the two pockets and the two tabs

Note: Units created this way will form inward-bulging triangular faces. To make them bulge outwards instead, replace the valley fold in Step 7 with a mountain fold. Steps 8-9 are similar but mirrored.

Assembly

When inserting units, line up the two red-marked parts so they overlap.

An important limitation is that each connection between two units can open to at most 90°, so Sturdy Edge Units can only form square or triangular faces. A hexagonal face is also possible by joining six coplanar triangles, though the result is less neat.

Remember that each Sturdy Edge Unit is an edge of the polyhedron. Feel free to explore the interactive visualizer to better understand polyhedron structures in 3D.

Two Sturdy Edge Units joined by inserting a tab of one unit into the pocket of the other, with the red marked parts of each unit overlapping

(The visualizer is functional but still under development.)