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For ultralow-loss and polarization-insensitive spot-size converters (SSCs) on a silicon platform, we propose and demonstrate a silicon knife-edge taper waveguide with a gradual decrease in height as well as width toward the taper end. The taper was fabricated using a double-patterning method involving i-line stepper photolithography and angled sidewall dry-etching. The SSC, with the knife-edge taper covered with a polymer secondary core, exhibited mode conversion losses of 0.35 and 0.21 dB for transverse electric-like and transverse magnetic-like modes, respectively.