A cw solution of acoustic diffraction by a three-sided semi-infinite barrier or a double edge, where the width of the midplanar segment is finite and cannot be ignored, involving all orders of diffraction is presented. The solution is an extension of the asymptotic formulas for the double-edge second-order diffraction via amplitude and phase matching given by Pierce [A. D. Pierce, J. Acoust. Soc. Am. 55, 943-955 (1974)]. The model accounts for all orders of diffraction and is valid for all kw, where k is the acoustic wave number and w is the width of the midplanar segment and reduces to the solution of diffraction by a single knife edge as w-->0. The theory is incorporated into the deformed edge solution [Stanton et al., J. Acoust. Soc. Am. 122, 3167 (2007)] to model the diffraction by a disk of finite thickness, and is compared with laboratory experiments of backscattering by elastic disks of various thicknesses and by a hard strip. It is shown that the model describes the edge diffraction reasonably well in predicting the diffraction as a function of scattering angle, edge thickness, and frequency.