In geometry, orbifold notation (or orbifold signature) is a system, invented by the mathematician William Thurston and promoted by John Conway, for representing...

the same wallpaper group; it is called p4m in the IUCr notation and *442 in the orbifold notation. Example C has a different wallpaper group, called p4g...

me. It was obtained by a democratic process in my course of 1976–77. An orbifold is something with many folds; unfortunately, the word "manifold" already...

named here by three naming schemes: International notation, orbifold notation, and Coxeter notation. There are three kinds of symmetry groups of the plane:...

arrangement (motif)). Orbifold notation (2D) Fibrifold notation (3D) As the name suggests, the orbifold notation describes the orbifold, given by the quotient...

vertical axis of symmetry. Also shown are Coxeter notation in brackets, and, in parentheses, orbifold notation. Chiral Cn, [n]+, (nn) of order n - n-fold rotational...

symmetry groups; its symmetry group in IUC notation as p4m, Coxeter notation as [4,4], and orbifold notation as *442. Two orientations of an image of the...

Misiurewicz–Thurston points Nielsen–Thurston classification Normal surface Orbifold notation Thurston norm Thurston's double limit theorem Thurston elliptization...

groups by Schoenflies notation, Coxeter notation, orbifold notation, and order. John Conway uses a variation of the Schoenflies notation, based on the groups'...

domains between two symmetry groups. They are compactly expressed in orbifold notation. These mutations can occur from spherical tilings to Euclidean tilings...

oblique lattice class names, Schönflies notation, Hermann-Mauguin notation, orbifold notation, Coxeter notation, and wallpaper groups are listed in the...

Schönflies notation, Hermann-Mauguin notation, point groups, International Tables for Crystallography space group number, orbifold notation, type, and...

three dimensions, each shown below in 3 notations: Schönflies notation, Coxeter notation, and orbifold notation. Chiral Dn, [n,2]+, (22n) of order 2n –...

translation. It can also be given a Schoenflies notation as S2∞, Coxeter notation as [∞+,2+], and orbifold notation as ∞×. In the Euclidean plane, reflections...

Schoenflies notation, Hermann–Mauguin (international) notation, orbifold notation, and Coxeter notation, type descriptors, mineral examples, and the notation for...

sphere to the Euclidean plane and into the hyperbolic plane. With orbifold notation symmetry of *n32 all of these tilings are wythoff construction within...

by their representations in international notation, Schoenflies notation, orbifold notation, Coxeter notation and mineral examples. There is only one tetragonal...

On successive lines are the orbifold notation, the Coxeter notation and Coxeter diagram, and the Hermann–Mauguin notation (full, and abbreviated if different)...

sphere to the Euclidean plane and into the hyperbolic plane. With orbifold notation symmetry of *n32 all of these tilings are wythoff construction within...

geometry into the study of knots with the hyperbolization theorem. The orbifold notation system, invented by Thurston, has been developed for representing...

hexagonal lattice class names, Schönflies notation, Hermann-Mauguin notation, orbifold notation, Coxeter notation, and wallpaper groups are listed in the...

polyhedron notation Conway triangle notation Orbifold notation This disambiguation page lists articles associated with the title Conway notation. If an internal...

mirrors at each triangle face vertex. This is *n32 in orbifold notation, and [n,3] in Coxeter notation. Conway, Symmetries of things, p.284 DisdyakisTriacontahedron...

triangle) at the points where the white curves cross. In John Conway's orbifold notation, this set of symmetries is denoted 433. Each fish provides a fundamental...

the wallpaper group of the lattice is given in IUCr notation, Orbifold notation, and Coxeter notation, along with a wallpaper diagram showing the symmetry...

Coxeter notation for S2n is [2n+,2+] and , as an index 4 subgroup of [2n,2], , generated as the product of 3 reflections. The Orbifold notation is n×,...

sphere to the Euclidean plane and into the hyperbolic plane. With orbifold notation symmetry of *n32 all of these tilings are Wythoff constructions within...

rectangular lattice class names, Schönflies notation, Hermann-Mauguin notation, orbifold notation, Coxeter notation, and wallpaper groups are listed in the...

the seven frieze groups describing the possible frieze patterns. Orbifold notation can be used to describe wallpaper groups of the Euclidean plane. Penrose...

tiling triangles represent the fundamental domains of p6m, [6,3] (*632 orbifold notation) wallpaper group symmetry. There are a number of small index subgroups...