Cuboctahedron

This shape can be created by weaving together four loops.

Step 1: Materials

Four strips of material and some clips.
I used construction paper cut into strips 12in long and 1.5in wide.

Step 2: First Loop

The first loop is the simplest. Just staple the two ends together.

Step 3: Second Loop

The second loop links through the first loop.

Step 4: Third Loop

The third loop is woven into the first two. I check the positioning on one side first making sure they all dive the same direction. I clip this shape together and line up the other side before stapeling. I then unclip to check that I got the weaving right. If it is woven correctly it will fall apart into the linkage shown below (if not it will look like more like a triangular prism).

Step 5: Fourth Loop

I realign the weaving and repin one side before moving on to the fourth loop. The fourth loop weaves over and under along the equator of the shape (try to weave under the pieces that want to pull inward and over the ones that pull outward). Once the shape is established the pins can be removed and the two ends of the fourth loop can be stapled together. Enjoy.

Going farther:
I've also made a smaller version with strips that half the width and go around twice (thereby eliminating staples). Using 3 times the strips at 1/3 the width I also made a more complex weave. I presume that increasingly complex weaves could be created indefinitely.