Allied & ICAR Exam Bank • ALLIED_2283 NAT • 2 Marks

Section 8: General Aptitude

Analytical & Spatial Aptitude

Subtopic: Spatial Reasoning & 3D Representations

Question Statement:

How many total proper rotational symmetries (orientation-preserving rotations) does a solid three-dimensional cube have in Euclidean space, including the identity rotation?

Answer Key:

24

Step-by-Step Solution & Explanation

The rotation group of a cube (isomorphic to the symmetric group S_4) contains exactly 24 elements: 1 identity, 9 rotations about face centers, 8 about body diagonals, 6 about edge midpoints. Total = 24.
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