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For which crystal system are all three edge lengths equal (a = b = c) AND all three interaxial angles equal (alpha = beta = gamma)?

1. Rhombohedral
2. Orthorhombic
3. Tetragonal
4. None of these

Correct answer: Rhombohedral

Solution

The rhombohedral (trigonal) crystal system has a = b = c and alpha = beta = gamma, where the common angle is not 90 deg. Cubic also satisfies a=b=c and alpha=beta=gamma=90 deg but is not offered as an option. Orthorhombic has a not equal to b not equal to c with alpha=beta=gamma=90 deg. Tetragonal has a=b not equal to c with alpha=beta=gamma=90 deg. Therefore Rhombohedral is the correct answer from the given choices.

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