|
Line Group
A line group is a mathematical way of describing symmetries associated with moving along a line. These symmetries include repeating along that line, making that line a one-dimensional lattice. However, line groups may have more than one dimension, and they may involve those dimensions in its isometries or symmetry transformations. One constructs a line group by taking a point group in the full dimensions of the space, and then adding translations or offsets along the line to each of the point group's elements, in the fashion of constructing a space group. These offsets include the repeats, and a fraction of the repeat, one fraction for each element. For convenience, the fractions are scaled to the size of the repeat; they are thus within the line's unit cell segment. One-dimensional There are 2 one-dimensional line groups. They are the infinite limits of the discrete two-dimensional point groups C''n'' and D''n'': Two-dimensional There are 7 frieze groups, which involve r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetry
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definition, and is usually used to refer to an object that is invariant under some transformations; including translation, reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are intricately related, and hence are discussed together in this article. Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including theoretic models, language, and music. This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frieze Group 1m
In architecture, the frieze is the wide central section part of an entablature and may be plain in the Ionic or Doric order, or decorated with bas-reliefs. Paterae are also usually used to decorate friezes. Even when neither columns nor pilasters are expressed, on an astylar wall it lies upon the architrave ("main beam") and is capped by the moldings of the cornice. A frieze can be found on many Greek and Roman buildings, the Parthenon Frieze being the most famous, and perhaps the most elaborate. This style is typical for the Persians. In interiors, the frieze of a room is the section of wall above the picture rail and under the crown moldings or cornice. By extension, a frieze is a long stretch of painted, sculpted or even calligraphic decoration in such a position, normally above eye-level. Frieze decorations may depict scenes in a sequence of discrete panels. The material of which the frieze is made of may be plasterwork, carved wood or other decorative medium. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wallpaper Group Diagram Pg Rotated
Wallpaper is a material used in interior decoration to decorate the interior walls of domestic and public buildings. It is usually sold in rolls and is applied onto a wall using wallpaper paste. Wallpapers can come plain as "lining paper" (so that it can be painted or used to help cover uneven surfaces and minor wall defects thus giving a better surface), textured (such as Anaglypta), with a regular repeating pattern design, or, much less commonly today, with a single non-repeating large design carried over a set of sheets. The smallest rectangle that can be tiled to form the whole pattern is known as the pattern repeat. Wallpaper printing techniques include surface printing, gravure printing, silk screen-printing, rotary printing, and digital printing. Wallpaper is made in long rolls which are hung vertically on a wall. Patterned wallpapers are designed so that the pattern "repeats", and thus pieces cut from the same roll can be hung next to each other so as to continue the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wallpaper Group Diagram Pm Rotated
Wallpaper is a material used in interior decoration to decorate the interior walls of domestic and public buildings. It is usually sold in rolls and is applied onto a wall using wallpaper paste. Wallpapers can come plain as "lining paper" (so that it can be painted or used to help cover uneven surfaces and minor wall defects thus giving a better surface), textured (such as Anaglypta), with a regular repeating pattern design, or, much less commonly today, with a single non-repeating large design carried over a set of sheets. The smallest rectangle that can be tiled to form the whole pattern is known as the pattern repeat. Wallpaper printing techniques include surface printing, gravure printing, silk screen-printing, rotary printing, and digital printing. Wallpaper is made in long rolls which are hung vertically on a wall. Patterned wallpapers are designed so that the pattern "repeats", and thus pieces cut from the same roll can be hung next to each other so as to continue the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wallpaper Group Diagram Cm
Wallpaper is a material used in interior decoration to decorate the interior walls of domestic and public buildings. It is usually sold in rolls and is applied onto a wall using wallpaper paste. Wallpapers can come plain as "lining paper" (so that it can be painted or used to help cover uneven surfaces and minor wall defects thus giving a better surface), textured (such as Anaglypta), with a regular repeating pattern design, or, much less commonly today, with a single non-repeating large design carried over a set of sheets. The smallest rectangle that can be tiled to form the whole pattern is known as the pattern repeat. Wallpaper printing techniques include surface printing, gravure printing, silk screen-printing, rotary printing, and digital printing. Wallpaper is made in long rolls which are hung vertically on a wall. Patterned wallpapers are designed so that the pattern "repeats", and thus pieces cut from the same roll can be hung next to each other so as to continue the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wallpaper Group Diagram Pm
Wallpaper is a material used in interior decoration to decorate the interior walls of domestic and public buildings. It is usually sold in rolls and is applied onto a wall using wallpaper paste. Wallpapers can come plain as "lining paper" (so that it can be painted or used to help cover uneven surfaces and minor wall defects thus giving a better surface), textured (such as Anaglypta), with a regular repeating pattern design, or, much less commonly today, with a single non-repeating large design carried over a set of sheets. The smallest rectangle that can be tiled to form the whole pattern is known as the pattern repeat. Wallpaper printing techniques include surface printing, gravure printing, silk screen-printing, rotary printing, and digital printing. Wallpaper is made in long rolls which are hung vertically on a wall. Patterned wallpapers are designed so that the pattern "repeats", and thus pieces cut from the same roll can be hung next to each other so as to continue the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wallpaper Group Diagram Pg
Wallpaper is a material used in interior decoration to decorate the interior walls of domestic and public buildings. It is usually sold in rolls and is applied onto a wall using wallpaper paste. Wallpapers can come plain as "lining paper" (so that it can be painted or used to help cover uneven surfaces and minor wall defects thus giving a better surface), textured (such as Anaglypta), with a regular repeating pattern design, or, much less commonly today, with a single non-repeating large design carried over a set of sheets. The smallest rectangle that can be tiled to form the whole pattern is known as the pattern repeat. Wallpaper printing techniques include surface printing, gravure printing, silk screen-printing, rotary printing, and digital printing. Wallpaper is made in long rolls which are hung vertically on a wall. Patterned wallpapers are designed so that the pattern "repeats", and thus pieces cut from the same roll can be hung next to each other so as to continue the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wallpaper Group Diagram P1 Rect
Wallpaper is a material used in interior decoration to decorate the interior walls of domestic and public buildings. It is usually sold in rolls and is applied onto a wall using wallpaper paste. Wallpapers can come plain as "lining paper" (so that it can be painted or used to help cover uneven surfaces and minor wall defects thus giving a better surface), textured (such as Anaglypta), with a regular repeating pattern design, or, much less commonly today, with a single non-repeating large design carried over a set of sheets. The smallest rectangle that can be tiled to form the whole pattern is known as the pattern repeat. Wallpaper printing techniques include surface printing, gravure printing, silk screen-printing, rotary printing, and digital printing. Wallpaper is made in long rolls which are hung vertically on a wall. Patterned wallpapers are designed so that the pattern "repeats", and thus pieces cut from the same roll can be hung next to each other so as to continue the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wallpaper Group
A wallpaper is a mathematical object covering a whole Euclidean plane by repeating a motif indefinitely, in manner that certain isometries keep the drawing unchanged. To a given wallpaper there corresponds a group of such congruent transformations, with function composition as the group operation. Thus, a wallpaper group (or plane symmetry group or plane crystallographic group) is in a mathematical classification of a two‑dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art, especially in textiles, tessellations and tiles as well as wallpaper. What this page calls pattern Any periodic tiling can be seen as a wallpaper. More particularly, we can consider as a wallpaper a tiling by identical tiles edge‑to‑edge, necessarily periodic, and conceive from it a wallpaper by decorating in the same manner every tiling element, and eventually erase partly or entirely the bou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schönflies Notation
The Schoenflies (or Schönflies) notation, named after the German mathematician Arthur Moritz Schoenflies, is a notation primarily used to specify point groups in three dimensions. Because a point group alone is completely adequate to describe the symmetry of a molecule, the notation is often sufficient and commonly used for spectroscopy. However, in crystallography, there is additional translational symmetry, and point groups are not enough to describe the full symmetry of crystals, so the full space group is usually used instead. The naming of full space groups usually follows another common convention, the Hermann–Mauguin notation, also known as the international notation. Although Schoenflies notation without superscripts is a pure point group notation, optionally, superscripts can be added to further specify individual space groups. However, for space groups, the connection to the underlying symmetry elements is much more clear in Hermann–Mauguin notation, so the latter not ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Point Groups In Three Dimensions
In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere. It is a subgroup of the orthogonal group O(3), the group of all isometries that leave the origin fixed, or correspondingly, the group of orthogonal matrices. O(3) itself is a subgroup of the Euclidean group E(3) of all isometries. Symmetry groups of geometric objects are isometry groups. Accordingly, analysis of isometry groups is analysis of possible symmetries. All isometries of a bounded (finite) 3D object have one or more common fixed points. We follow the usual convention by choosing the origin as one of them. The symmetry group of an object is sometimes also called its full symmetry group, as opposed to its proper symmetry group, the intersection of its full symmetry group with E+(3), which consists of all ''direct isometries'', i.e., isometries preserving orientation. For a bounded object, the proper sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.svg "Click for more on -> Symmetry")
