  A well-known and interesting family of sub-Riemannian space are the systems
involving two balls rolling against each other without slipping or twisting. In
this note, we show how the sub-Riemannian geodesics of these space, when the
two balls are embedded in $\mathbb{R}^3 \times \mathbb{R}^3$, are horizontal
curves on the intersections of these balls with Euclidean 5-planes.
