  The shape of semiflexible polymer rings is studied over their whole range of
flexibility. Investigating the joint distribution of asphericity and nature of
asphericity as well as their respective averages we find two distinct shape
regimes depending on the flexibility of the polymer. For small perimeter to
persistence length the fluctuating rings exhibit only planar, elliptical
configurations. At higher flexibilities three dimensional, crumpled structures
arise. Analytic calculations for tight polymer rings confirm an elliptical
shape in the stiff regime.
