  We construct a new subsystem code in three dimensions that exhibits
single-shot error correction in a user-friendly and transparent way. As this
code is a subsystem version of coupled toric codes, we call it the intertwined
toric code (ITC). Although previous codes share the property of single-shot
error correction, the ITC is distinguished by its physically motivated origin,
geometrically straightforward logical operators and errors, and a simple phase
diagram. The code arises from 3d stabilizer toric codes in a way that
emphasizes the physical origin of the single-shot property. In particular,
starting with two copies of the 3d toric code, we add check operators that
provide for the confinement of pointlike excitations without condensing the
loop excitations. Geometrically, the bare and dressed logical operators in the
ITC derive from logical operators in the underlying toric codes, creating a
clear relationship between errors and measurement outcomes. The syndromes of
the ITC resemble the syndromes of the single-shot code by Kubica and Vasmer,
allowing us to use their decoding schemes. We also extract the phase diagram
corresponding to ITC and show that it contains the phases found in the
Kubica-Vasmer code. Finally, we suggest various connections to Walker-Wang
models and measurement-based quantum computation.
