Ultra-narrow bandgap III-V semiconductor nanomaterials provide a unique platform for realizing advanced nanoelectronics, thermoelectrics, infra-red photodetection and quantum transport physics. In this work we employ molecular beam epitaxy to synthesize novel nanosheet-like InSb nanostructures exhibiting superior electronic performance. Through careful morphological and crystallographic characterization we show how this unique geometry is the result of a single twinning event in an otherwise pure zinc blende structure. Four-terminal electrical measurements performed in both the Hall and van der Pauw configurations reveal a room temperature electron mobility greater than 12,000 cm(2).V(-1).s(-1). Quantized conductance in a quantum point contact processed with a split-gate configuration is also demonstrated. We thus introduce InSb 'nanosails' as a versatile and convenient platform for realizing new device and physics experiments with a strong interplay between electronic and spin degrees of freedom.