An acoustic attenuator for a turbomachine and methodology for additively manufacturing the acoustic attenuator are provided. The acoustic attenuator includes an annular body (202) having an outer surface (204) and an inner surface (206). The inner surface of the annular body may define a bore (208) extending along a longitudinal axis (209) of the acoustic attenuator between a first end and a second end of the acoustic attenuator. The annular body may be formed by a plurality of axially-successive cross-sectional layers (e.g., 632, 634, 636) unitized between the first end and the second end of the acoustic attenuator. The plurality of axially-successive cross-sectional layers may be transversely disposed relative to the longitudinal axis of the acoustic attenuator. At least some axially-successive cross-sectional layers of the plurality of axially-successive cross-sectional layers (e.g., 632, 634, 636) defining a pocket (214) disposed between the outer surface and the inner surface of the annular body. At least a segment of a periphery of the pocket comprises two sides (1452, 1454) arranged to join at a common end point to form an apex (1460) of the pocket.