three kinds of symmetry groups of the plane: 2 families of rosette groups – 2D point groups 7 frieze groups – 2D line groups 17 wallpaper groups – 2D space...
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simpler frieze groups and the three-dimensional space groups. A proof that there are only 17 distinct groups of such planar symmetries was first carried...
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point group Triangle group List of planar symmetry groups Point groups in two dimensions Johnson, 2015 Conway, John H. (2008). The symmetries of things...
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photographic lens designed by Paul Rudolph at Carl Zeiss in 1896 List of planar symmetry groups Planarity, a computer puzzle game Plane (disambiguation) Planer (disambiguation)...
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In geometry, circular symmetry is a type of continuous symmetry for a planar object that can be rotated by any arbitrary angle and map onto itself. Rotational...
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Symmetry (from Ancient Greek συμμετρία (summetría) 'agreement in dimensions, due proportion, arrangement') in everyday life refers to a sense of harmonious...
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described by Lie groups while discrete symmetries are described by finite groups (see Symmetry group). These two concepts, Lie and finite groups, are the foundation...
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molecular symmetry describes the symmetry present in molecules and the classification of these molecules according to their symmetry. Molecular symmetry is a...
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groups arise naturally in the study of symmetries and geometric transformations: The symmetries of an object form a group, called the symmetry group of...
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Order-6 hexagonal tiling (redirect from 333333 symmetry)
Order-6 hexagonal tiling. Square tiling Tilings of regular polygons List of uniform planar tilings List of regular polytopes Weisstein, Eric W. "Hyperbolic...
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Truncated order-4 octagonal tiling (redirect from 882 symmetry)
Uniform tiling 4-16-16. Square tiling Tilings of regular polygons List of uniform planar tilings List of regular polytopes Weisstein, Eric W. "Hyperbolic...
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(4 3 3) *433 symmetry (4 4 3) *443 symmetry (4 4 4) *444 symmetry (5 4 2) *542 symmetry (6 4 2) *642 symmetry ... The above symmetry groups only include...
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polygons List of uniform planar tilings List of regular polytopes John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5...
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Order-8 triangular tiling (redirect from 444 symmetry)
of regular polygons List of uniform planar tilings List of regular polytopes John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things...
7 KB (359 words) - 21:56, 12 December 2023
Truncated order-6 square tiling (redirect from 443 symmetry)
of regular polygons List of uniform planar tilings List of regular polytopes John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things...
4 KB (270 words) - 21:58, 12 December 2023
Order-4 heptagonal tiling (redirect from 2^7 symmetry)
Order-4 heptagonal tiling. Square tiling Tilings of regular polygons List of uniform planar tilings List of regular polytopes Weisstein, Eric W. "Hyperbolic...
3 KB (289 words) - 21:56, 12 December 2023
Order-4 pentagonal tiling (redirect from 22222 symmetry)
Order-4 pentagonal tiling. Square tiling Tilings of regular polygons List of uniform planar tilings List of regular polytopes Weisstein, Eric W. "Hyperbolic...
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line groups, and polychromatic plane groups are derived and illustrated. Loeb's synthetic approach does not enable a comparison of colour symmetry concepts...
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Order-8 octagonal tiling (redirect from 44444444 symmetry)
of regular polygons List of uniform planar tilings List of regular polytopes John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things...
2 KB (224 words) - 21:58, 12 December 2023
Order-8 square tiling (redirect from 4444 symmetry)
tilings in hyperbolic plane List of regular polytopes John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5...
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Infinite-order apeirogonal tiling (redirect from I^i symmetry)
regular polygons List of uniform planar tilings List of regular polytopes John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008...
3 KB (191 words) - 21:53, 12 December 2023
Polyhedron (redirect from Volume of a polyhedron)
polyhedron. Realizations that omit the requirement of face planarity, that impose additional requirements of symmetry, or that map the vertices to higher dimensional...
87 KB (9,849 words) - 08:10, 8 August 2024
Crystallographic restriction theorem (category Group theory)
system allowing for infinite rotational symmetry). The strength of the theorem is that not all finite groups are compatible with a discrete lattice; in...
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Truncated infinite-order triangular tiling (redirect from I33 symmetry)
Wikimedia Commons has media related to Uniform tiling 6-6-i. List of uniform planar tilings Tilings of regular polygons Uniform tilings in hyperbolic plane John...
2 KB (170 words) - 21:56, 12 December 2023
Truncated order-4 hexagonal tiling (redirect from 662 symmetry)
Uniform tiling 4-12-12. Square tiling Tilings of regular polygons List of uniform planar tilings List of regular polytopes Weisstein, Eric W. "Hyperbolic...
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Octahedron (section Uniform colorings and symmetry)
three-dimensional symmetry groups, the octahedral symmetry O h {\displaystyle \mathrm {O} _{\mathrm {h} }} . The surface area A {\displaystyle A} of a regular...
33 KB (3,297 words) - 12:32, 28 July 2024
Truncated order-8 hexagonal tiling (redirect from 664 symmetry)
8-12-12. Tilings of regular polygons List of uniform planar tilings John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008,...
5 KB (343 words) - 21:58, 12 December 2023
Rhombitetraapeirogonal tiling (redirect from I222 symmetry)
of regular polygons List of uniform planar tilings List of regular polytopes John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things...
3 KB (186 words) - 21:57, 12 December 2023
Rhombitetrahexagonal tiling (redirect from 3222 symmetry)
*3322 symmetry. Wikimedia Commons has media related to Uniform tiling 4-4-4-6. Square tiling Tilings of regular polygons List of uniform planar tilings...
5 KB (343 words) - 21:57, 12 December 2023
Order-4 apeirogonal tiling (redirect from Iiii symmetry)
of regular polygons List of uniform planar tilings List of regular polytopes John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things...
4 KB (252 words) - 22:49, 27 May 2024