1. An LED luminaire comprising:one or more light-emitting diodes (LEDs) emitting light of a plurality of discrete colors; and
a single element light collimator optically coupled to the one or more LEDs, the collimator comprising:
a light receiving end with a general geometric shape that is the same as the general shape of the cross sectional shape of the LED(s) with straight edges, which transitions into a geometric shape with curved edges rotationally displaced from the cross-sectional shape orientation of the LED die; and
a plurality of at least three sides curved in a cross-section perpendicular to the primary axis of the collimated and mixed light exiting the collimator.