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8 9 rAdiAl centred symmetries Radial symmetries are probably the most familiar of all regular arrangements. Being finite, they belong to the broad category of point group symmetriesand they come in three distinct forms. In 2dimensions they are centred on a point in the plane, showing rotational symmetry, with any number of regular divisions of the circle reflection is also frequently incorporated, creating dihedral symmetries 1. Many flowers show this arrangement, and of course centred, radial motifs appear in the decorative art of practically every culture. In 3dimensions, radial symmetries are either centred on a point in space, where each path fans out from the centre to every outlying point as in an explosion 2 or they have a polar axis of rotation, typically cylindrical or conical 3. These last are the characteristic symmetries of plants. The great majority of flowers have petal arrangements using a number taken from the Fibonacci series, i.e. 3, 5, 8, 13, 21 etc. more on this magical sequence on pg. 30. The celebrated symmetry of snow crystals, by contrast, is always sixpointed. As well as being a favoured symmetry of decorative motifs, planarradial symmetry is also the most useful configuration for any device involving rotary motionparticularly the wheel in its various manifestations. Radial symmetries of all kinds, being finite, belong to the category of pointgroup symmetries 1. 2d radial symmetry 2. 3d radial symmetry 3. Radial symmetries around a polar axis
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