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The Symmetries of Things

door John H. Conway

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Start with a single shape. Repeat it in some way--translation, reflection over a line, rotation around a point--and you have created symmetry. Symmetry is a fundamental phenomenon in art, science, and nature that has been captured, described, and analyzed using mathematical concepts for a long time. Inspired by the geometric intuition of Bill Thurston and empowered by his own analytical skills, John Conway, with his coauthors, has developed a comprehensive mathematical theory of symmetry that allows the description and classification of symmetries in numerous geometric environments. This richly and compellingly illustrated book addresses the phenomenological, analytical, and mathematical aspects of symmetry on three levels that build on one another and will speak to interested lay people, artists, working mathematicians, and researchers.… (meer)
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Have you ever exploited symmetry in your own designs, proofs, or organizational solutions? Of course the answer is "yes": symmetry is one of the deepest principles of human mind. In the form of conservation laws, it literally provides the basis for much of modern physics. But don't worry, this book is not about physics! It is a heavily illustrated book about the math behind symmetry.

Conway has created a wonderful example of graphical clarity and geometric thinking about regular patterns and tilings. Don't be put off by his coinage of goofy terms; he successfully presents deep mathematics via purely visual proofs. Furthermore, he turns the old way of presenting symmetry on its head, starting with geometry and topology, and only later addressing group theory.

This book is highly recommended to anyone who is interested in how symmetry works. Some understanding of group theory would be helpful, but the graphics alone make perusing the book worthwhile. ( )
1 stem ztutz | Oct 15, 2009 |
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Wikipedia in het Engels (247)

10-10 duoprism

10-demicube

10-simplex

120-gon

3-3 duoprism

List of H4 polytopes

List of planar symmetry groups

List of spherical symmetry groups

Michael Guy

Octadecagon

Octagonal tiling

Octagram

Octahedral prism

Octahedral symmetry

Orbifold notation

Order-2 apeirogonal tiling

Order-3 apeirogonal tiling

Order-4 apeirogonal tiling

Order-4 heptagonal tiling

Order-4 hexagonal tiling

Order-4 octagonal tiling

Order-4 pentagonal tiling

Order-5 apeirogonal tiling

Order-5 hexagonal tiling

Order-5 pentagonal tiling

Order-5 square tiling

Order-6 hexagonal tiling

Order-6 octagonal tiling

Order-6 pentagonal tiling

Order-6 square tiling

Order-7 heptagonal tiling

Order-7 heptagrammic tiling

Order-7 square tiling

Order-7 triangular tiling

Order-8 hexagonal tiling

Order-8 octagonal tiling

Order-8 square tiling

Order-8 triangular tiling

Pentaapeirogonal tiling

Pentadecagon

Pentagon

Pentahexagonal tiling

Pentakis icosidodecahedron

Pentakis snub dodecahedron

Point groups in four dimensions

Polygram (geometry)

Proprism

Quarter cubic honeycomb

Quarter order-6 square tiling

Rectification (geometry)

Rectified 24-cell

Rectified 5-cell

Rectified truncated cube

Rectified truncated dodecahedron

Rectified truncated icosahedron

Rectified truncated octahedron

Rectified truncated tetrahedron

Regular 4-polytope

Regular skew apeirohedron

Rhombihexaoctagonal tiling

Rhombille tiling

Rhombipentahexagonal tiling

Rhombitetraapeirogonal tiling

Rhombitetraheptagonal tiling

Rhombitetrahexagonal tiling

Rhombitetraoctagonal tiling

Rhombitetrapentagonal tiling

Rhombitriapeirogonal tiling

Rhombitriheptagonal tiling

Rhombitrihexagonal tiling

Rhombitrioctagonal tiling

Runcinated tesseracts

Runcination

Skew apeirohedron

Small stellated 120-cell

Snub (geometry)

Snub 24-cell

Snub apeiroapeirogonal tiling

Snub heptaheptagonal tiling

Snub hexahexagonal tiling

Snub hexaoctagonal tiling

Snub octaoctagonal tiling

Snub order-6 square tiling

Snub order-8 triangular tiling

Snub pentahexagonal tiling

Snub pentapentagonal tiling

Snub rhombicuboctahedron

Snub square tiling

Snub tetraapeirogonal tiling

Snub tetraheptagonal tiling

Snub tetrahexagonal tiling

Snub tetraoctagonal tiling

Snub tetrapentagonal tiling

Snub triapeirogonal tiling

Snub triapeirotrigonal tiling

Snub triheptagonal tiling

Snub trihexagonal tiling

Snub trioctagonal tiling

Square tiling

Star polyhedron

Template:Convex prismatic prisms

Tetraapeirogonal tiling

Tetracontadigon

Tetracontaoctagon

Tetradecagon

Tetrahedral prism

Tetrahedral symmetry

Tetrahedral-octahedral honeycomb

Tetraheptagonal tiling

Tetrahexagonal tiling

Tetrakis cuboctahedron

Tetrakis square tiling

Tetraoctagonal tiling

Tetrapentagonal tiling

Triacontadigon

Triakis truncated tetrahedral honeycomb

Triakis truncated tetrahedron

Triangular tiling

Triapeirogonal tiling

Triaprism

Trigonal trapezohedral honeycomb

Triheptagonal tiling

Trihexagonal tiling

Trioctagonal tiling

Truncated heptagonal tiling

Truncated hexagonal tiling

Truncated hexaoctagonal tiling

Truncated infinite-order square tiling

Truncated infinite-order triangular tiling

Truncated octagonal tiling

Truncated order-3 apeirogonal tiling

Truncated order-4 apeirogonal tiling

Truncated order-4 heptagonal tiling

Truncated order-4 hexagonal tiling

Truncated order-4 octagonal tiling

Truncated order-4 pentagonal tiling

Truncated order-5 hexagonal tiling

Truncated order-5 pentagonal tiling

Truncated order-5 square tiling

Truncated order-6 hexagonal tiling

Truncated order-6 octagonal tiling

Truncated order-6 pentagonal tiling

Truncated order-6 square tiling

Truncated order-7 heptagonal tiling

Truncated order-7 square tiling

Truncated order-7 triangular tiling

Truncated order-8 hexagonal tiling

Truncated order-8 octagonal tiling

Truncated order-8 triangular tiling

Truncated pentahexagonal tiling

Truncated rhombicosidodecahedron

Truncated rhombicuboctahedron

Truncated square tiling

Truncated tesseract

Truncated tetraapeirogonal tiling

Truncated tetraheptagonal tiling

Truncated tetrahexagonal tiling

Truncated tetraoctagonal tiling

Truncated tetrapentagonal tiling

Truncated triapeirogonal tiling

Truncated triheptagonal tiling

Truncated trihexagonal tiling

Truncated trioctagonal tiling

Uniform 4-polytope

Uniform antiprismatic prism

Uniform k 21 polytope

Uniform tiling symmetry mutations

Uniform tilings in hyperbolic plane

Vertex configuration

Start with a single shape. Repeat it in some way--translation, reflection over a line, rotation around a point--and you have created symmetry. Symmetry is a fundamental phenomenon in art, science, and nature that has been captured, described, and analyzed using mathematical concepts for a long time. Inspired by the geometric intuition of Bill Thurston and empowered by his own analytical skills, John Conway, with his coauthors, has developed a comprehensive mathematical theory of symmetry that allows the description and classification of symmetries in numerous geometric environments. This richly and compellingly illustrated book addresses the phenomenological, analytical, and mathematical aspects of symmetry on three levels that build on one another and will speak to interested lay people, artists, working mathematicians, and researchers.

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