Symmetry pp 243-253 | Cite as

Cosmological symmetries


The symmetries of polyhedra were primarily rotational. Turned around one of their axes of symmetry, they would overlap themselves. A body displaying n-fold symmetry around a given axis will, after n rotations, not just overlap itself in terms of the space taken up by its shape, but really return to exactly the same position: if we mark a particular point on it (e.g. the one we use to rotate it), it will return to the same place. If we continue to repeat the rotations of angle 2π/n, oneachnth occasion we will return to the same position (though, unless we place a mark on the polyhedron, we will not be able to distinguish the intermediate stages from one another). During the rotation, that is, the shape will periodically repeat itself.


Planetary Orbit Approximate Symmetry Sine Curve Summer Solstice Maximum Sustained Wind 
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© Birkhäuser Verlag AG 2007

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