The total number of symmetry elements in the crystal class represented by the point group 4/m3 2/m is:
Show Hint
- 21
- 22
- 23
- 24
The Correct Option is D
Solution and Explanation
Step 1: Identify the crystal class.
The point group 4/m 3 2/m belongs to the isometric (cubic) system, specifically the octahedral class (also called the full cubic symmetry).
Step 2: List symmetry elements.
The octahedral (4/m 3 2/m) class contains:
- Axes of rotation:
- 3 fourfold axes (along cube axes),
- 4 threefold axes (along cube body diagonals),
- 6 twofold axes (along cube face diagonals).
Total = 13 rotational axes.
- Mirror planes:
- 9 mirror planes (3 axial, 6 diagonal).
- Center of symmetry:
- 1 inversion center.
- Rotoinversion/symmetry combinations:
- These generate the full set such that the total count = 24 distinct symmetry elements.
Step 3: Confirm standard reference.
In crystallography tables, the point group 4/m 3 2/m (Oh) is known to have the maximum possible symmetry elements: 24.
Final Answer:
\[
\boxed{24}
\]
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