In a previous paper (q.v.) by Mr W. L. Marr and the present writer, it was shown that, in accordance with Morley's Theorem, the angles A+2pπ, B+2pπ, C+2rπ of the triangles ABC be trisected, the three groups of six lines at the vertices give rise to 27 triangles DEF, the biangular coordinates of D with respect to BC being (B/3+2qπ/3, C/3+2rπ/3) or (βq, γr), and similarly for and F with respect to CA and AB.