Using rapid prototyping, we manufacture an acoustic horn designed by gradient-based shape optimization to have virtually perfect impedance-matching properties. The horn is 161.5 mm long, has a mouth diameter of 300 mm, and a throat diameter intended for a 1.5 inch driver. We optimize the horn with the aim of having perfect radiation efficiency at 31 frequencies in the range 1.6–9.05 kHz, while satisfying a convexity constraint on the flare. The acoustical properties, as needed by the optimization algorithm, are calculated through numerical solutions with the finite-element method of the axisymmetric Helmholtz equation. The prototype has been analyzed in an anechoic chamber. In the design frequency band, the acoustic input impedance agrees reasonably well with the ideal characteristic impedance of a waveguide with the same cross sectional area as the horn throat.