A lighting apparatus includes a polygon die including a plurality of light-emitting diodes (LEDs), and a submount to which each of the LEDs is coupled. Each LED includes a plurality of epi-layers which contains a p-type layer, an n-type layer, and a multiple quantum well (MQW) disposed between the p-type layer and the n-type layer, and a p-type electrode and an n-type electrode which are electrically coupled to the p-type layer and the n-type layer, respectively. The p-type and the n-type electrodes are located between the submount and the epi-layers. The submount contains a plurality of conductive elements configured to electrically couple at least a portion of the plurality of LEDs in series. At least some of the plurality of LEDs have non-rectangular top view shapes.