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CHROMATIC PLANE ORNAMENTS
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17 ornamental affine group affine transformation arithmetic class arithmetic group automorphism basis u,v bijective calculate cartesian coordinate mapping cartesian form chromatic plane ornaments classification Clearly COALQ computation conditions A1 conjugacy class conjugate consonant contained cosets course defined denote determined equal equivalence classes euclidean group euclidean plane euclidean transformation exists a member Figure finite subgroup foregoing geometric class Hence hexagonal inner automorphism invariant Let f let Q Let us assume Let us consider linear mapping mapping carrying matrix member 9 Moreover mosaic Q n-chromatic homomorphism n-chromatic mosaic normal subgroup obtain ORBKT ornamental classes ornamental groups ornamental subgroup plane crystal positive integer positive real number principal measure problem Proof Proposition Prove quadratic refer reflection relation of isomorphism relative to u,v satisfies conditions semi-direct product stand SUBMT subset surjective symmetries of Q symmetry group symmorphic Table 12 THEOREM tion translational and linear yield Z.vA Z.uA