Methods and apparatus for fabricating structures, extrusion units, and structures fabricated using such methods and apparatus are disclosed. The apparatus may include a support configured for rotation about a central axis, a carriage that may move along the support when the support rotates about the central axis such that the carriage may move along a first spiral path about the central axis, and an extrusion unit that may be supported by the carriage and may move along a second spiral path as the carriage moves along the first spiral path. The extrusion units may be configured to extrude a strip of material through an extrusion die as the extrusion unit moves along a previously extruded strip of material such that the extruded strip may be fused onto the previously extruded strip as the extruded and previously extruded strips pass the extrusion die.