This paper addresses two challenges in establishing a new process chain for polishing hexagonal segments for extremely large telescopes:- i) control of edge and corner profiles in small-tool polishing of hexagons, and ii) achieving the required smoothness of the bulk aspheric form. We briefly describe the performance of a CNC-grinding process used to create the off-axis asphere, which established the input-quality for subsequent processing. We then summarize processes for smoothing ground mid-spatials and pre- and corrective polishing using Zeeko CNC machines. The impact of two cases is considered; i) all processing stages are performed after the segment is cut hexagonal, and ii) final rectification of a hexagon after cutting from an aspherised roundel, as an alternative to ionfiguring. We then report on experimental results on witness samples demonstrating edges and corners close to the EELT segment specification, and results on a full-aperture spherical segment showing excellent surface smoothness.