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Definitions of aiguillette:
noun: An ornamental braided cord with decorative metal tips worn on uniforms.
noun: Alternative form of aiglet (“metal tip on a ribbon or cord that facilitated lacing two parts of a garment together”) [A tip, originally of metal and often decorative, on a ribbon or cord that makes lacing two parts of a garment or garments together easier, as in corset lacings, "points" (lacing hose or trousers to jacket or doublet) or sleeves to a bodice.]