A solid state light source with LEDs in thermal contact to thermally conductive translucent elements where light emitted from the LEDs is directed to emerge from the heat dissipating surfaces of the elements. The thermally conductive translucent elements are arranged or combined with a reflector to form a light recycling cavity. The outside surfaces of the thermally conductive translucent elements forming the cavity become luminescent as the light emitted by the LEDs on the inside of the cavity is continually reflected and recycled until a very high percentage of the light emitted by the LEDs is eventually transmitted through and emitted uniformly and omnidirectionally. Simultaneously, the heat from the LEDs conducts through and to the luminescent outside surfaces of the elements of the cavity, which radiatively and convectively cool the light source thereby eliminating the need for bulky appended heat sinks.