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Of the various phases of transition alumina, iota-alumina (ι-Al2O3) is the least well known. It is considered to be the end member of the mullite series in the limit of zero Si content. The structural details of ι-Al2O3 are not available and its physical properties are totally unknown. Based on an appropriately modified structure of a high alumina content mullite phase close to the 9-1 mullite, we have successfully constructed a structural model for ι-Al2O3. The simulated x-ray diffraction (XRD) pattern of this model agrees well with a measured XRD pattern obtained from samples that claim to belong to ι-Al2O3. ι-Al2O3 is a highly disordered ultralow-density phase of alumina with a theoretical density of 2854 kg/m3. The calculated total energy per Al2O3 is much higher than α-Al2O3 and the other well-known disordered phase, γ-Al2O3. Using this theoretically constructed model, we have calculated the elastic, thermodynamic, electronic, and spectroscopic properties of ι-Al2O3 and compared them with those of α-Al2O3 and γ-Al2O3. It is shown that the mechanical strength of ι-Al2O3 is much weaker with bulk and shear moduli that are only 57 and 42% of α-Al2O3. Phonon dispersion results and the subsequently calculated thermodynamic properties point to the fact that ι-Al2O3 is an alumina phase preceding γ-Al2O3 in the processing of alumina before reaching α-Al2O3. Electronic structure calculations show it to be an insulator with a direct band gap of only 3.0 eV at the Γ point and a higher ionic bonding character than α-Al2O3 and γ-Al2O3. It has a calculated static dielectric constant of 2.73 and a corresponding refractive index of 1.65 that are in agreement with reported data. Also calculated are the Al-K, Al-L3, and O-K edges of the x-ray absorption near edge structure in ι-Al2O3, showing sensitive dependence on its local bonding environment. However, only the weighted average of these spectra can be directly compared with the measured ones which are currently unavailable.