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...

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

the 17 groups plus a number of non-periodic tilings Wikimedia Commons has media related to Wallpaper group diagrams. List of planar symmetry groups (summary...

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...

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

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

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

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...

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...

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

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

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,...

(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...

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...

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

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

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...

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

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...

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...

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

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,...

*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...

4] symmetry, and 7 with subsymmetry. Wikimedia Commons has media related to Uniform tiling 4-8-16. Tilings of regular polygons List of uniform planar tilings...

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