  Epitaxial growth of thin-film heterostructures is generally considered the
most successful procedure to obtain interfaces of excellent structural and
electronic quality between three-dimensional materials. However, these
interfaces can only join material systems with crystal lattices of matching
symmetries and lattice constants. We present a novel category of interfaces,
the fabrication of which is membrane-based and does not require epitaxial
growth. These interfaces therefore overcome limitations imposed by epitaxy.
Leveraging the additional degrees of freedom gained, we demonstrate atomically
clean interfaces between three-fold symmetric sapphire and four-fold symmetric
SrTiO3. Atomic-resolution imaging reveals structurally well-defined interfaces
with a novel moir\'e-type reconstruction.
