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How to define a Tensor with the symmetries like Riemann tensor?

The skew symmetries and the interchange symmetry can be implemented easily by specifying them as symmetry generators in SymmetrizedArray: ...
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Doing ArrayReshape in Mathematica doesn't give desired results

The array in matrix-form can sometimes be misleading, if you call the indexes of the tensor properly, you'll see that it's similar to other languages that use Row-Major ordering (e.g., Python) to ...
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Doing ArrayReshape in Mathematica doesn't give desired results

Try this: Map[Transpose, ArrayReshape[a, {2, 2, 2, 2}]] // MatrixForm
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