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Published in:
2007 | OriginalPaper | Chapter
Cosmological symmetries
Published in: Symmetry
Publisher: Birkhäuser Basel
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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
, oneach
n
th 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.