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We analyze the spectrum of the 11.2 µm unidentified infrared band (UIR) from NGC 7027 and identify a small fullerene (C₂₄) as a plausible carrier. The blurring effects of lifetime and vibrational anharmonicity broadening obscure the narrower, intrinsic spectral profiles of the UIR band carriers. We use a spectral deconvolution algorithm to remove the blurring, in order to retrieve the intrinsic profile of the UIR band. The shape of the intrinsic profile-a sharp blue peak and an extended red tail-suggests that the UIR band originates from a molecular vibration-rotation band with a blue band head. The fractional area of the band-head feature indicates a spheroidal molecule, implying a nonpolar molecule and precluding rotational emission. Its rotational temperature should be well approximated by that measured for nonpolar molecular hydrogen, ∼825 K for NGC 7027. Using this temperature, and the inferred spherical symmetry, we perform a spectral fit to the intrinsic profile, which results in a rotational constant implying C₂₄ as the carrier. We show that the spectroscopic parameters derived for NGC 7027 are consistent with the 11.2 µm UIR bands observed for other objects. We present density functional theory (DFT) calculations for the frequencies and infrared intensities of C₂₄. The DFT results are used to predict a spectral energy distribution (SED) originating from absorption of a 5 eV photon, and characterized by an effective vibrational temperature of 930 K. The C₂₄ SED is consistent with the entire UIR spectrum and is the dominant contributor to the 11.2 and 12.7 µm bands.