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Silicon carbide (SiC) supports surface phonons in the infrared region of the electromagnetic spectrum where these modes can be thermally emitted. Additionally, the magnitude, spectrum, and direction of thermal radiation from SiC can be controlled by engineering this material at the sub-wavelength scale. For these reasons, SiC nanopillars are of high interest for thermal-radiation tuning. So far, theoretical and experimental studies of thermal emission from SiC nanopillars have been limited to long-pitch arrays with a microscale interpillar spacing. It is not clear how far-field thermal emission from SiC nanopillars is affected when the interparticle spacing reduces to the nanometer scale, where the near-field interaction between adjacent nanopillars arises and the array becomes zero order. In this Letter, we study physical mechanisms of far-field thermal radiation from zero-order arrays of silicon-carbide nanopillars with a nanoscale interpillar spacing. We show that the increased volume of thermal emitters and thermal radiation of the hybrid waveguide-surface-phonon-polariton mode from zero-order arrays increase the spectral emissivity of silicon carbide to values as large as 1 for a wide range of angles. The enhanced, dispersion-less thermal emission from a zero-order SiC array of nano-frustums with an optimized interspacing of 300 nm is experimentally demonstrated. Our study provides insight into thermal radiation from dense nanostructures and has significant implications for thermal management of electronic devices and energy harvesting applications.