  Elucidating the symmetry of intertwined orders in exotic superconductors is
at the quantum frontier. Recent surface sensitive studies of the topological
kagome superconductor CsV$_3$Sb$_5$ discovered a cascade 4a$_0$ superlattice
below the charge density wave (CDW) ordering temperature, which can be related
to the pair density modulations in the superconducting state. If the 4a$_0$
phase is a bulk and intrinsic property of the kagome lattice, this would form a
striking analogy to the stripe order and pair density wave discovered in the
cuprate high-temperature superconductors, and the cascade ordering found in
twisted bilayer graphene. High-resolution X-ray diffraction has recently been
established as an ultra-sensitive probe for bulk translational
symmetry-breaking orders, even for short-range orders at the diffusive limit.
Here, combining high-resolution X-ray diffraction, scanning tunneling
microscopy and scanning transmission electron microscopy, we demonstrate that
the 4a$_0$ superstructure emerges uniquely on the surface and hence exclude the
4a$_0$ phase as the origin of any bulk transport or spectroscopic anomaly.
Crucially, we show that our detected 2$\times$2$\times$2 CDW order breaks the
bulk rotational symmetry to C2, which can be the driver for the bulk nematic
orders and nematic surface superlattices including the 4a$_0$ phase. Our
high-resolution data impose decisive spatial symmetry constraints on emergent
electronic orders in the kagome superconductor CsV$_3$Sb$_5$.
