An analytic expression is derived for the radiation view factor between two arbitrarily oriented planar triangles and, by a simple generalization, planar polygons. Unlike most attempts so far, which use the contour integration technique, Nusselt's unit sphere method is used in this work. Two important features of the analytical expression derived here are that: (1) the use of numerical quadrature is not necessary for the computation, and (2) the symmetry of the expression ensures that reciprocity of view factors is preserved. (C) 2015 Elsevier Ltd. All rights reserved.