Last Update 18/ 05/ 2000
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The special presentation of ordered repetition forms along one or more directions in space either following straight lines, planes or several curves attracted the attention of people. The organization of diverse materials in vegetable, animal and mineral reign is explained by well defined mathematical rules, its study enables comprehension of a nature's face. In chemistry symmetry related properties are studied with analytical objectives, such that the sequential exhibition of the parts is expected to lead to information on the focalized object and simplifies its identification. One of the investigation possibilities uses to rotate the sample. If the same image is observed repeatedly before the 360 o or 2p radians turn is completed, a symmetry axis is present. Several other symmetry elements exists beyond the rotation axis, as for example the symmetry plane, inversion centre, inversion and rotation axis and reflection and rotation axis, screw axis and glide planes, including translation in space. After any object is rotated 2p radians around an axis the same image is observed as before the execution of this operation. This is a trivial identity operation. If the object develops the same image after turning p radians around an axis, it is named two fold rotation axis, represented by C2 or 2, according to Schoenflies or to Hermann-Maugin notation. The figure shows the ethene molecule, represented by two black spheres in the place of the two carbon atoms double bonded, two blue spheres bonded to each carbon atom, representing the four hydrogen atoms. Any line represents a bond from one atom to another. Different groups, indicated by different colours on the spheres can replace the original blue spheres by clicking on the buttons labeled A=X; A=B=X; A=C=X; A=D=X; A=X, B=Y; A=X, C=Y; A=X, D=Y. Different sphere colours indicate different chemical groups. If you push and drag the mouse properly when the cursor is over the green square, you can animate the molecule to a sequence of rotation positions. Half turn on the molecule can be performed after a click on the button 0 o and 180 o. It will be interesting to verify the existence or absence of C2 in the given orientation in the eight kinds of selected molecules, with four equal groups or with one or two different groups at your choice by clicking on the buttons at the right.
Bibliography
SHUBNIKOV, A.V. and KOPTSIK, V.A., Symmetry in Science and Art, Plenum Press, N.Y., 1974.
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