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...

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

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

Uniform tiling 6-10-10. 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...

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

LCCN 99035678. Square tiling Tilings of regular polygons List of uniform planar tilings List of regular polytopes Weisstein, Eric W. "Hyperbolic tiling". MathWorld...

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-4 pentagonal 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...

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...

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,...

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

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

regular tiling of the hyperbolic plane. It has Schläfli symbol of {5,6}. This regular tiling can also be constructed from [(5,5,3)] symmetry alternating...

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,...

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

there are 7 forms with full [6,5] symmetry, and 3 with subsymmetry. Tilings of regular polygons List of uniform planar tilings John H. Conway, Heidi Burgiel...

(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...

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...

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

regular tiling of the hyperbolic plane with a Schläfli symbol of {3,7}. The symmetry group of the tiling is the (2,3,7) triangle group, and a fundamental...

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