Discussion
Minimum symmetry that a cubic crystal must possess is
Answer: A
A cubic crystal must have four 3-fold rotation axes.
The defining symmetry of the cubic system is four three-fold axes along the body diagonals of the cube. Every cubic point group, including the lowest one (23, tetrahedral rotations only), has them.
Three 4-fold axes are present only in the higher cubic classes (432 and m3m), not in all, so they are not the minimum. Three orthogonal mirror planes or a centre of symmetry are likewise absent from some cubic classes (for example 23 has neither), and many non-cubic crystals have them.
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