In mathematics, a frieze or frieze pattern is a two-dimensional design that repeats in one direction. The term is derived from architecture and decorative arts, where such repeating patterns are often used. (See frieze.) Frieze patterns can be classified into seven types according to their symmetries. The set of symmetries of a frieze pattern is called a frieze group.
Frieze groups are two-dimensional line groups, having repetition in only one direction. They are related to the more complex wallpaper groups, which classify patterns that are repetitive in two directions, and crystallographic groups, which classify patterns that are repetitive in three directions.
friezegroups, listed in the summary table. Many authors present the friezegroups in a different order. The actual symmetry groups within a frieze group...
Glide-reflection symmetry is seen in friezegroups (patterns which repeat in one dimension, often used in decorative borders), wallpaper groups (regular tessellations...
isomorphic to the standard group C = C∞ and to Z, the additive group of the integers. An example is the first friezegroup. Here there are no finite cycles...
alone was almost 20 metres (65' 11/16") wide. The base was decorated with a frieze in high relief showing the battle between the Giants and the Olympian gods...
The Parthenon frieze is the high-relief Pentelic marble sculpture created to adorn the upper part of the Parthenon's naos. It was sculpted between c. 443...
symmetry groups of the plane: 2 families of rosette groups – 2D point groups 7 friezegroups – 2D line groups 17 wallpaper groups – 2D space groups. There...
along the axis a discrete point group, friezegroup, or wallpaper group in a plane, combined with any symmetry group in the perpendicular direction all...
dihedral group represents the friezegroup symmetry, p1m1, seen as an infinite set of parallel reflections along an axis. Every dihedral group is generated...
R2) such that the group contains both Tv and Tw. The purpose of this condition is to distinguish wallpaper groups from friezegroups, which possess a translation...
Friezegroups are magnetic 1D line groups and layer groups are magnetic wallpaper groups, and the axial 3D point groups are magnetic 2D point groups....
There are 7 friezegroups in two dimensions, consisting of symmetries of the plane whose group of translations is isomorphic to the group of integers...
subgroup of a Hausdorff group is closed. every discrete subgroup of a compact Hausdorff group is finite. Friezegroups and wallpaper groups are discrete subgroups...
the group under consideration. Groups representable in this notation include the point groups on the sphere ( S 2 {\displaystyle S^{2}} ), the frieze groups...
The Frieze of Parnassus is a large sculpted stone frieze encircling the podium, or base, of the Albert Memorial in London, England. The Albert Memorial...
Crystal system Friezegroup Isometry Lattice Point group Point groups in two dimensions Point groups in three dimensions Space group Symmetry group Translational...
dihedral group of S1. Non-bounded figures may have isometry groups including translations; these are: the 7 friezegroups the 17 wallpaper groups for each...
The Bassae Frieze is the high relief marble sculpture in 23 panels, 31 m long by 0.63 m high, made to decorate the interior of the cella of the Temple...
wallpaper group and one is in p4m. Tilings in 2-D with translational symmetry in just one direction may be categorized by the seven friezegroups describing...
of the group. The orbifold notation is a unified notation, also applicable for wallpaper groups and friezegroups. The crystallographic groups have n...
one-dimensional line groups. They are the infinite limits of the discrete two-dimensional point groups Cn and Dn: There are 7 friezegroups, which involve reflections...
the object. They are the finite symmetry groups on a cone. For n = ∞ they correspond to four friezegroups. Schönflies notation is used. The terms horizontal...
groups, organized by crystal system or lattice type, and by their point groups: Point group Crystallographic point group Space group Rod groupFrieze...
Frieze Art Fair is an annual contemporary art fair first held in 2003 in London's Regent's Park. Developed by the founders of the contemporary art magazine...
out as a wallpaper with a wallpaper group such as pmm, while the border may be laid out as a frieze of friezegroup pm11, pmm2 or pma2. Turkish and Central...
algebroid Lattice (group) Lattice (discrete subgroup) Friezegroup Wallpaper group Space group Crystallographic group Fuchsian group Modular group Congruence...
are 8 enantiomorphic pairs. Point group Crystallographic point group Space group Line groupFriezegroup Layer group Hitzer, E.S.M.; Ichikawa, D. (2008)...
Examples of groups List of the 230 crystallographic 3D space groups Examples of Markov chains Examples of vector spaces Fano plane Friezegroup Gray graph...
of reflection groups, rotational symmetry, friezegroups that describe border patterns repeating in one direction, and wallpaper groups that describe...
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