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X(1), X(357), X(358), X(1136), X(1137) excenters vertices A3, B3, C3 of Morley (third) triangle (green) vertices A3*, B3*, C3* of adjunct Morley (third) triangle, isogonal conjugates of A3, B3, C3. 

The cubic K031 is analogous to K029 Morley (first) cubic. It is an isogonal pK obtained when the trisectors of A, B, C are replaced by those of A2π, B2π, C2π. See also table 9 : Morley & Co. 
