Cover

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Title Page, Frontispiece, Copyright

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Preface and Biographic Remarks

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pp. v-vi

Starting from the somewhat vague notion of symmetry = harmony of proportions, these four lectures gradually develop first the geometric concept of symmetry in its several forms, as bilateral, translatory, rotational, ornamental and crystallographic symmetry, etc., and finally rise to the general idea underlying all these special forms, namely that of invariance of a configuration of elements under a group of automorphic transformations. ...

Contents

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pp. vii-viii

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Bilateral symmetry

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pp. 3-40

If I am not mistaken the word symmetry is used in our everyday language in two meanings. In the one sense symmetric means something like well-proportioned, well-balanced, and symmetry denotes that sort of concordance of several parts by which they integrate into a whole. ...

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Translatory, rotational, and related symmetries

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pp. 41-82

From bilateral we shall now turn to other kinds of geometric symmetry. Even in discussing the bilateral type I could not help drawing in now and then such other symmetries as the cylindrical or the spherical ones. ...

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Ornamental symmetry

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pp. 83-118

This lecture will have a more systematic character than the preceding one, in as much as it will be dedicated to one special kind of geometric symmetry, the most complicated but also the most interesting from every angle. In two dimensions the art of surface ornaments deals with it, in three dimensions it characterizes the arrangement of atoms in a crystal. ...

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Crystals. The general mathematical idea of symmetry

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pp. 119-146

In the last lecture we considered for two dimensions the problem of making up a complete list (i) of all orthogonally inequivalent finite groups of homogeneous orthogonal transformations, (ii) of all such groups as have invariant lattices, (iii) of all unimodularly inequivalent finite groups of homogenous transformations with integral coefficients, ...

Appendices

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pp. 147-148

A. Determination of all finite groups of proper rotations in 3-space

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pp. 149-154

B. Inclusion of improper rotations

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pp. 155-156

Acknowledgments

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pp. 157-160

Index

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pp. 161-168