Brunnian links consist of $n$ linked un-knot components such that the cutting of any component leaves all components unconnected. The most famous example is the three-component Borromean rings (or links). In 1954 Milnor classified all Brunnian links up to link homotopy.

In $\mathbb{R}^3$, it is simple indeed to see that one can construct Borromean rings from identical *rigid* components. (The simplest case involves three identical rigid ovals---same intrinsic shape, same intrinsic size.) I have sketched six classes of rigid (un-knot) components that can be linked to form Borromean rings, and I'm sure there are an infinite number of such.

**Question**

Is it possible to create identical rigid components interlocked to form **Brunnian links** for $n \geq 4$? Is there an upper limit for $n$ for which this can be done?