An (Al, Ga, In)N light emitting diode (LED) in which multi-directional light can be extracted from one or more surfaces of the LED before entering a shaped optical element and subsequently being extracted to air. In particular, the (Al, Ga, In)N and transparent contact layers (such as ITO or ZnO) are embedded in or combined with a shaped optical element comprising an epoxy, glass, silicon or other material molded into an inverted cone shape, wherein most of the light entering the inverted cone shape lies within a critical angle and is extracted. In addition, the present invention stands the LED on end, i.e., rotates the position of the LED within the shaped optical element by approximately 90° as compared to a conventional LED, in order to extract light more effectively from the LED. The present invention also minimizes internal reflections within the LED by eliminating mirrors and/or mirrored surfaces, in order to minimize re-absorption of the LED's light by the emitting layer (or the active layer) of the LED. To assist in minimizing internal reflections, transparent electrodes, such as ITO or ZnO, may be used. Surface roughening by patterning or anisotropically etching (i.e., creating microcones) may also assist in light extraction, as well as minimizing internal reflections.