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Affine Isomorphism

  • Page ID
    17795
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    Each symmetry operation of crystallographic group in E3 may be represented by a 3×3 matrix W (the linear part) and a vector w. Two crystallographic groups G1 = {(W1i,w1i)} and G2 = {(W2i,w2i)} are called affine isomorphic is there exists a non-singular 3×3 matrix A and a vector a such that:

    G2 = {(A,a)(W1i,w1i)(A,a)-1}

    Two crystallographic groups are affine isomorphic if and only if their arrangement of symmetry elements may be mapped onto each other by an affine mapping of E3. Two affine isomorphic groups are always isomorphic.


    Affine Isomorphism is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Online Dictionary of Crystallography.

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