Cyclohexane exhibits rotational symmetry?

Cyclohexane exhibits these conformations because it doesn't conform to a perfect hexagonal shape. The bonds are not at 109.5 degrees, causing angle strain to the 2D planar hexagon. Torsional strain is also considerable due to the eclipsed bonds. So, in order to reduce this strain, cyclohexane adopts the 3D structure--chair conformation, which puts the carbons all at angles of 109.5 degrees. This allows for the most stable structure of cyclohexane.