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...

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...

point group Triangle group List of planar symmetry groups Point groups in two dimensions Johnson, 2015 Conway, John H. (2008). The symmetries of things...

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)...

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...

Symmetry (from Ancient Greek συμμετρία (summetría) 'agreement in dimensions, due proportion, arrangement') in everyday life refers to a sense of harmonious...

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...

molecular symmetry describes the symmetry present in molecules and the classification of these molecules according to their symmetry. Molecular symmetry is a...

groups arise naturally in the study of symmetries and geometric transformations: The symmetries of an object form a group, called the symmetry group of...

(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...

Uniform tiling 4-16-16. Square tiling Tilings of regular polygons List of uniform planar tilings List of regular polytopes Weisstein, Eric W. "Hyperbolic...

line groups, and polychromatic plane groups are derived and illustrated. Loeb's synthetic approach does not enable a comparison of colour symmetry concepts...

Order-6 hexagonal tiling. Square tiling Tilings of regular polygons List of uniform planar tilings List of regular polytopes Weisstein, Eric W. "Hyperbolic...

Order-4 heptagonal tiling. Square tiling Tilings of regular polygons List of uniform planar tilings List of regular polytopes Weisstein, Eric W. "Hyperbolic...

isometry groups in the plane including the frieze groups and wallpaper groups, and the classification of two-dimensional patterns by their symmetries. Another...

of regular polygons List of uniform planar tilings List of regular polytopes John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things...

Order-4 pentagonal tiling. Square tiling Tilings of regular polygons List of uniform planar tilings List of regular polytopes Weisstein, Eric W. "Hyperbolic...

regular polygons List of uniform planar tilings List of regular polytopes John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008...

of regular polygons List of uniform planar tilings List of regular polytopes John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things...

4-8-12. Tilings of regular polygons List of uniform planar tilings John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008,...

polyhedron. Realizations that omit the requirement of face planarity, that impose additional requirements of symmetry, or that map the vertices to higher dimensional...

of regular polygons List of uniform planar tilings List of regular polytopes John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things...

system allowing for infinite rotational symmetry). The strength of the theorem is that not all finite groups are compatible with a discrete lattice; in...

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...

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...

of regular polygons List of uniform planar tilings List of regular polytopes John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things...

media related to Uniform tiling 6-16-16. Tilings of regular polygons List of uniform planar tilings List of regular polytopes Weisstein, Eric W. "Hyperbolic...

Uniform tiling 4-12-12. Square tiling Tilings of regular polygons List of uniform planar tilings List of regular polytopes Weisstein, Eric W. "Hyperbolic...

three-dimensional symmetry groups, the octahedral symmetry O h {\displaystyle \mathrm {O} _{\mathrm {h} }} . The surface area A {\displaystyle A} of a regular...

of regular polygons List of uniform planar tilings List of regular polytopes John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things...