  We present a hyperspectral cube of the Crab Nebula obtained with the imaging
Fourier transform spectrometer SITELLE on the Canada-France-Hawaii telescope.
We describe our techniques used to deconvolve the 310 000 individual spectra (R
= 9 600) containing Halpha, [NII]6548,6583, and [SII]6716,6731 emission lines
and create a detailed three-dimensional reconstruction of the supernova remnant
assuming uniform global expansion. We find that the general boundaries of the
3D volume occupied by the Crab are not strictly ellipsoidal as commonly
assumed, and instead appear to follow a "heart-shaped" distribution that is
symmetrical about the plane of the pulsar wind torus. Conspicuous restrictions
in the bulk distribution of gas consistent with constrained expansion coincide
with positions of the dark bays and east-west band of He-rich filaments, which
may be associated with interaction with a pre-existing circumstellar disk. The
distribution of filaments follows an intricate honeycomb-like arrangement with
straight and rounded boundaries at large and small scales that are
anti-correlated with distance from the center of expansion. The distribution is
not unlike the large-scale rings observed in supernova remnants 3C 58 and
Cassiopeia A, where it has been attributed to turbulent mixing processes that
encouraged outwardly expanding plumes of radioactive 56Ni-rich ejecta. These
characteristics reflect critical details of the original supernova of 1054 CE
and its progenitor star, and may favour a low-energy explosion of an iron-core
progenitor. We demonstrate that our main findings are robust despite regions of
non-homologous expansion driven by acceleration of material by the pulsar wind
nebula.
