This seems the result of an intriguing combination of the symmetry design principle with a total lack of rotational symmetry, decentrations and misalignments of the optical surfaces.

Natural forms that grow or move perpendicular to the earth’s surface develop rotational symmetry.

The state progressions are selected such that they can be represented by a diagram having 90° rotational symmetry.

It consists of the familiar translational symmetry, rotational symmetry and the inertial reference frame invariance central to the theory of special relativity.

Therefore, the global Poincaré symmetry, consisting of translational symmetry, rotational symmetry and the inertial reference frame invariance central to the theory of special relativity must apply.

Note that these additional symmetries do not allow a planar slice to have, say, 8-fold rotation symmetry.

Thus 5-fold rotational symmetry cannot be eliminated by an argument missing either of those assumptions.

They ensure, among other things, that the rotational symmetry of the original polyhedron is preserved, and that each stellation is different in outward appearance.

Upon this inherently symmetrical starting point, potters from ancient times onwards have added patterns that modify the rotational symmetry to achieve visual objectives.

The housing has an interior cavity which is preferably spherical but need only be partially spherical, the remainder at least having rotational symmetry.

Various electrical connectors each include respective signal nodes and power nodes arranged in accordance with a ninety-degree rotational symmetry.

The method may include receiving a plug at a receptacle, the receptacle including contacts disposed with a rotational symmetry about a center point of the receptacle.

It consists of the rotations in Cn, together with reflection symmetry in n axes that pass through the center.

It consists of the rotations in Cn (there is rotational symmetry of order n), together with reflection symmetry in n axes that pass through the center.

At that time, the ruling paradigm about crystal structures stated that all crystals are periodic and therefore have only a one-, two-, three-, four- or sixfold rotation symmetry.