illustris

The drawing and metaphor are from a paper submitted to the Royal Society in 1660 by Sir Robert Moray. He was a natural philosopher and co-founder of the Royal Society together with - inter alios - Prince Rupert of the Rhine who brought the so-called Bolognese or Dutch tears to England. Nowadays they are familiar as Rupert drops. These are taking shape when a blob of molten glass has fallen into cold water. Such droplets are showing high strength under compression. In the movie on the left (5,000 fps) it resists a load of 20 tons before it bursts. In the movie below (96,000 fps) a bullet is shot against the vertex of a pending droplet. The projectile gets fragmented, its debris is scattered in a conical shape. Within micro-seconds after the impact the droplet is decomposing into tiny particles starting from the tip of its tail. In the movie on the right this process is shown in ultra slow motion. In that experiment a bullet was shot at the droplet's tail, somewhere at point "C" in Moray's drawing. The tail or the "head" in the metaphor, respectively, is the Achilles heel of the whole body and its failure causes a catastrophic breakdown.

The thermal quenching yields a rapidly solidifying outer layer (approx. 10% of the volume) which features an exceptional high strength under compressive load. Due to the liquid-solid transition the outer layer is shrinking (increased density of the solid) which causes a high compressive stress that has to be overcome for crack initiation. Those still being created are deflected at the interface with the inner phase which still has conserved tensile stress from the melt flow. At the thinned tail disturbances can easily reach the tension zone. Cracks than propagate with speeds in the order of 10^3 m/s and are spreading via bifurcations throughout the entire volume.

Prince Rupert of the Rhine also became known for winning a bet in the late 1660s: one cube fits through a second cube of the same size or slightly smaller (max. 4% difference). A mathematical proof was later provided and over time it was found that this was possible with every pair of identical convex polyhedra. Nevertheless, with increasing number of sides, the margins for the tunneling are getting sometimes very small. The movie shows the passage for a row of Platonic solids. However, the first Noperthedron was reported recently this year (Nopert = none Rupert).

Original article: J. Steininger and S. Yurkevich, A convex polyhedron without Rupert's property. arXiv:2508.18475v1

Further Reading: E. Klarreich, First Shape Found That Can't Pass Through Itself, Quanta, October 24, 2025