  We classify all exactly stress-free solutions to the cubic-to-trigonal phase
transformation within the geometrically linearized theory of elasticity,
showing that only simple laminates and crossing-twin structures can occur. In
particular, we prove that although this transformation is closely related to
the cubic-to-orthorhombic phase transformation, all its solutions are rigid.
The argument relies on a combination of the Saint-Venant compatibility
conditions together with the underlying nonlinear relations and non-convexity
conditions satisfied by the strain components.
