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We present a hyperspectral cube of the Crab Nebula obtained with the imagingFourier 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 linesand create a detailed three-dimensional reconstruction of the supernova remnantassuming uniform global expansion. We find that the general boundaries of the3D volume occupied by the Crab are not strictly ellipsoidal as commonlyassumed, and instead appear to follow a "heart-shaped" distribution that issymmetrical about the plane of the pulsar wind torus. Conspicuous restrictionsin the bulk distribution of gas consistent with constrained expansion coincidewith positions of the dark bays and east-west band of He-rich filaments, whichmay be associated with interaction with a pre-existing circumstellar disk. Thedistribution of filaments follows an intricate honeycomb-like arrangement withstraight and rounded boundaries at large and small scales that areanti-correlated with distance from the center of expansion. The distribution isnot unlike the large-scale rings observed in supernova remnants 3C 58 andCassiopeia A, where it has been attributed to turbulent mixing processes thatencouraged outwardly expanding plumes of radioactive 56Ni-rich ejecta. Thesecharacteristics reflect critical details of the original supernova of 1054 CEand its progenitor star, and may favour a low-energy explosion of an iron-coreprogenitor. We demonstrate that our main findings are robust despite regions ofnon-homologous expansion driven by acceleration of material by the pulsar windnebula.

3D mapping of the Crab Nebula with SITELLE. I. Deconvolution and kinematic reconstruction