### Some articles on *symmetry, fold, fold rotational symmetry, rotational symmetry*:

Crystallographic Restriction Theorem - Dimensions 2 and 3 - Lattice Proof

... A rotation

... A rotation

**symmetry**in dimension 2 or 3 must move a lattice point to a succession of other lattice points in the same plane, generating a regular polygon of coplanar lattice points ... and swirling in geometric patterns.) Now consider an 8-**fold**rotation, and the displacement vectors between adjacent points of the polygon ... small as we like thus no discrete lattice can have 8-**fold**symmetry ...Point Groups In Three Dimensions - The Seven Infinite Series of Axial Groups

... which can be any integer in each series, the nth

... which can be any integer in each series, the nth

**symmetry**group contains n-**fold rotational symmetry**about an axis, i.e ...**symmetry**with respect to a rotation by an angle 360°/n ... n=1 covers the cases of no**rotational symmetry**at all ...### Famous quotes containing the words symmetry and/or fold:

“What makes a regiment of soldiers a more noble object of view than the same mass of mob? Their arms, their dresses, their banners, and the art and artificial *symmetry* of their position and movements.”

—George Gordon Noel Byron (1788–1824)

“When the inhabitants of some sequestered island first descry the “big canoe” of the European rolling through the blue waters towards their shores, they rush down to the beach in crowds, and with open arms stand ready to embrace the strangers. Fatal embrace! They *fold* to their bosoms the vipers whose sting is destined to poison all their joys; and the instinctive feeling of love within their breasts is soon converted into the bitterest hate.”

—Herman Melville (1819–1891)

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