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.
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