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...

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

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...

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

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...

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...

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

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

Order-6 hexagonal tiling. 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...

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...

triangular tiling Tilings of regular polygons List of uniform tilings John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5...

the symmetry of second derivatives (also called the equality of mixed partials) is the fact that exchanging the order of partial derivatives of a multivariate...

*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...

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

more for the mirror image. It has point symmetry, also known as rotational symmetry of order 2. Its symmetry group has two elements, the identity and the...

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...

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

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...

tiling of the hyperbolic plane with a Schläfli symbol of tr{∞,3}. The dual of this tiling represents the fundamental domains of [∞,3], *∞32 symmetry. There...

three-dimensional symmetry groups, the octahedral symmetry O h {\displaystyle \mathrm {O} _{\mathrm {h} }} . The regular octahedron is one of the Platonic...

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