A modular heat sink includes one or more heat sink sections interconnected sequentially to each other to form a polar array. Each heat sink section includes a first connecting part and a second connecting part, where the first connecting part is configured to couple with the second connecting part of another heat sink section. Once assembled, the modular heat sink includes a channel formed substantially through the center of the modular heat sink. Each heat sink section is manufactured using an extrusion process. The assembled modular heat sink has one or more hollow portions within the overall shape that cannot be fabricated in a single extrusion process. One or more LEDs are coupled to the outer surface of the modular heat sink. The modular heat sink, with LEDs coupled thereto, is coupled to a wireway tube and mounted to a post-top light fixture to form an LED luminaire.