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Topic: Wallpaper group

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	The Discontinuous Groups of Rotation and Translation in the Plane (Site not responding. Last check: 2007-10-10)
		Group category 2.2.2.1: Contain non-parallel translations and rotations where the least positive angle is 2*π/2.
		Group category 2.2.2.2: Contain non-parallel translations and rotations where the least positive angle is 2*π/3.
		Group category 2.2.2.5: Contain non-parallel translations and rotations where the least positive angle is not one of 2*π/n with n = {2,3,4,6}.
	www.xahlee.org /Wallpaper_dir/c0_WallPaper.html (155 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal (Site not responding. Last check: 2007-10-10)
		A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern.
		Wallpaper groups are two-dimensional symmetry groups, intermediate in complexity between the simpler frieze groups and the three-dimensional crystallographic groups (also called space groups).
		The wallpaper group of a pattern is invariant under isometries and uniform scaling (similarity transformations).
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Wallpaper_group (3809 words)

	Wallpaper group - Wallpapergroup
		Wallpaper groups are related to the simpler frieze groups, and to the more complex three-dimensional crystallographic groups (also called space groups).
		This wallpaper group corresponds to the case that all triangles of the same orientation are equal, while both types have rotational symmetry of order three, and both are symmetric, but the two are not equal, and not each other's mirror image.
		This wallpaper group corresponds to the case that all triangles of the same orientation are equal, while both types have rotational symmetry of order three and are each other's mirror image, but not symmetric themselves, and not equal.
	www.kopete.org /Wallpaper-group.html (4361 words)

	The Seventeen Wallpaper Groups
		A wallpaper group is a discontinuous subgroup of the isometries of the Euclidian plane.
		Wallpaper groups are distiguished from another type of transformation pattern of the plane called "tilings" by the fact that only a single pattern does the tiling of the plane in each group.
		The fundamental region of this group is also the translation region, hence the unit lengths of the translation vectors correspond to the lengths of two intersecting edges of the fundamental region.
	jwilson.coe.uga.edu /EMT668/EMAT6680.F99/McCallum/WALLPA~1/SEVENT~1.HTM (3603 words)

	wallpaper group
		Also known as a crystallographic group, a distinct way to tile the plane that repeats indefinitely in two dimensions; that is, a collection of two-dimensional symmetric patterns on a plane surface, containing two nonparallel translations (see periodic tiling).
		There are only 17 kinds of these patterns, known as isometries, each uniquely identified by its translation and rotation symmetries, as discovered in the late nineteenth century by E. Fedorov and, independently, by the German A. Schoenflies and the Englishman William Barlow.
		Every two-dimensional repetitive pattern in wallpaper, textiles, brickwork, or the arrangement of atoms in a plane of a crystal is just a minor variations on one of these 17 patterns.
	www.daviddarling.info /encyclopedia/W/wallpaper_group.html (203 words)

	Symmetry in Oriental Carpets
		Although it is possible to understand the wallpaper groups, or symmetry groups, without the knowledge of graphical transformations, it is very interesting to follow the graphical implications of patterns in oriental carpets and to see the relationship between graphical transformation and rug patterns.
		The IUC notation for the wallpaper group was established in 1952 by the International Union of Crystallography.
		The eleventh symmetry group (IUC notation is p3m1) consists of a reflection and rotation of 120°.
	www.ccds.charlotte.nc.us /2005hpc12/symmetry_in_oriental_carpets.htm (2212 words)

	NationMaster - Encyclopedia: Tessellation (Site not responding. Last check: 2007-10-10)
		FACTOID # 55: Australians are the most likely to join charities, educational organizations, environmental groups, sports groups and unions.
		Two intersecting planes in three-dimensional space In mathematics, a plane is a two-dimensional manifold or surface that is perfectly flat.
		Tesselations can be seen in almost every brick wall, tiled floor or wall, quilt pattern, lace tablecloth, fabric and wallpaper pattern.
	www.nationmaster.com /encyclopedia/Tessellation (561 words)

	Xah: Wall Paper Groups (Site not responding. Last check: 2007-10-10)
		Group category 2.2.2.1: Contain non-parallel translations and rotations where the least positive angle is 2*π/2.
		Group category 2.2.2.2: Contain non-parallel translations and rotations where the least positive angle is 2*π/3.
		Group category 2.2.2.4: Contain non-parallel translations and rotations where the least positive angle is not one of 2*π/n with n = {2,3,4,6}.
	xahlee.org /Wallpaper_dir/c0_WallPaper.html (145 words)

	Wallpaper: Get high res wallpapers from Flickr - Lifehacker
		Wallpapr's not bad, and it serves its purpose, but you can also just as easily cut out the middle man and search the Flickr Wallpapers Group directly on Flickr.
		And while you're looking for wallpaper on Flickr, you'll definitely want to check out the Wallpaper exchange group started here on Lifehacker, which continues to thrive with great images for your desktop delights.
		My favorite wallpaper is a deep, dark royal blue, or my wallpaper template made in Illustrator that partitions my screen into file-type zones, which I use during longer projects that tend to clutter my desktop with lots of temporary files.
	www.lifehacker.com /software/wallpaper/get-high-res-wallpapers-from-flickr-208810.php (388 words)

	Xah: Wallpaper: The 17 Wallpaper Groups
		For example, the group 442 consists of two distinct sets of 4-fold rotations and a set of 2-fold rotations.
		Roughly speaking, an orbifold is the quotient of a manifold by a discrete group acting on it.
		The wallpaper design is obtained by applying all symmetry elements to an L shaped motif.
	xahlee.org /Wallpaper_dir/c5_17WallpaperGroups.html (672 words)

	2.4 Wallpaper Groups
		A group of symmetries of the plane that is doubly infinite is a crystallographic group, or wallpaper group.
		The Conway notation for wallpaper groups is based on what types of non-translational symmetries occur in the ``simplest description'' of the group: * indicates a reflection (mirror symmetry), ×; a glide-reflection, and a number n indicates a rotational symmetry of order n (rotation by 360°/n).
		The last column of the table gives the number of degrees of freedom in the choice of the group, that is, the dimension of the space of inequivalent groups of the given type (equivalent groups are those that can be obtained from one another by proportional scaling or rigid motion).
	www.geom.uiuc.edu /docs/reference/CRC-formulas/node12.html (596 words)

	Flickr: Flickr desktop wallpaper swap - Lifehacker
		Inspired by Lifehacker's Desktop Show and Tell Holiday Giveaway, loyal reader Vince Broerman has started a new Flickr group for exchanging those cool desktop wallpapers (ranging from serene to extreme) he's seen on all of your desktop screencaps.
		So check out the Wallpaper Exchange Flickr group, add your awesome desktop wallpaper, and snag a few other wallpapers posted by fellow Lifehackers.
		For example, this one is one of the default wallpapers that ships with OS X. This one even carries a Warner Bros copyright statement in the lower right corner.
	www.lifehacker.com /software/flickr/flickr-desktop-wallpaper-swap-143976.php (268 words)

	3.3 The Wallpaper Groups
		In the presented analysis we distinguished 17 different cases for the wallpaper groups: 2 for the oblique, 6 for rectangular, 7 for centered, 11 for square, and 11 for hexagonal lattice.
		The remaining groups pm and cm are not mutually isomorphic, because every glide reflection from pm can be decomposed as the product of translations and reflections from pm (Theorem 3.2, Corollary 3.2), which is not true for cm.
		Finally, the group pmm is not isomorphic with pmg or cmm, because every glide reflection from pmm can be decomposed as the product of translations and reflections belonging to that group (Theorem 3.2, Corollary 2), which not holds for pmg or cmm.
	www.mi.sanu.ac.yu /vismath/ana/ana6.htm (1290 words)

	CVM 1.1 (VW): Color-turning wallpaper (Site not responding. Last check: 2007-10-10)
		A wallpaper with group p3 whose colors are interchanged by certain rotations of 120 degrees.
		Still, this is not the simplest color-turning wallpaper, because it has color-preserving half-turns in addition to the color-turning 3-centers.
		The fl borders on this one occur because the values of the wallpaper function become very high and are thus colored fl.
	www.maa.org /cvm/1998/01/vw/article/viewing/ctw.html (200 words)

	NY Review of Magazines (Site not responding. Last check: 2007-10-10)
		*Wallpaper’s** affluent audience of 25- to 40-year-old men and women in 50 different countries makes the magazine an advertiser’s dream.
		Recovering in London from gunshot wounds suffered while on assignment in Afghanistan, Brûlé hatched the idea for Wallpaper* as he leafed through magazines that he thought were "rubbish." After just four issues, Time Inc. purchased the magazine for $1.63 million in June 1997; Brûlé retained a 15 percent interest and his role as editorial director.
		In fact, the Wallpaper Group is its own division within the AOL Time Warner empire, run from a ravishingly stylish suite of offices in London.
	www.jrn.columbia.edu /studentwork/nyrm/2001/reviews/wallpaper.html (557 words)

	Cool Solutions: Restricting Wallpaper using Group Policies and ZENworks
		Before creating a Group Policy to manage the desktop wallpaper, you must create a wallpaper file you want to use and place it in a standard location.
		This will bring up the Group Policies window on the machine you are working on (You must perform this on a machine with the OS that you will be modifying -- Windows 2000 or XP).
		In the User or Workstation Package Group Policy window, select the tab for Policy Schedule and adjust the event for when you wan the policies to be set on the machine.
	www.novell.com /coolsolutions/feature/3281.html (536 words)

	Management Today - Article - Full Details (Site not responding. Last check: 2007-10-10)
		Based in London, Ware will head the Wallpaper Group advertising and commercial teams in the UK and across its eight international offices, which include New York, Paris and Hong Kong.
		Starting in June, he is also due to oversee Wallpaper magazine, the new bi-annual travel title, Navigator, and the development of the soon-to-be-launched Wallpaper website.
		Ware joins from PHD Media where, for the past four years, he was a group head on brands including Sainsbury's and The Economist.
	www.clickmt.com /public/news/index.cfm?fuseaction=fulldetails&newsuid=709e8a4a-f62f-434e-aede-c5de89fb6c72 (223 words)

	The Design of 2-Colour Wallpaper Patterns Using Methods Based on Chaotic Dynamics and Symmetry
		In the case of wallpaper patterns, there is also a choice of one- or two-color symmetry.
		At this point it is customary to divide the lattice subgroups into five classes (oblique, rectangular, centered rectangular (or rhombic), square and hexagonal) and then classify the wallpaper groups according to the point groups that can occur for each lattice class.
		Suppose G is a wallpaper group with associated point group J. For simplicity we suppose that G
	arpam.free.fr /mfield.html (5289 words)

	[No title]
		Stripping wallpaper is one of the most tedious tasks in all of redecorating, but it's a necessary and rewarding chore.
		Each wallpaper present on mota.ru can be removed on request from the author.
		In "The Yellow Wallpaper," John is an example of husband as patriarch, as his efforts to help his wife is a result of seeing women as less than adult.
	www.lycos.com /info/wallpaper.html (441 words)

	CVM 1.1 (VW): Informal Discussion of Anti-Symmetries (Site not responding. Last check: 2007-10-10)
		Recall that the symmetries for any wallpaper group can all be represented as compositions of a few, selected
		This has to be done in a consistent way so that when you compose symmetries, the tag for the composition of the two symmetries is the product of their tags.
		Of course these groups are infinite, but in some sense G has to be exactly half of E.
	www.maa.org /cvm/1998/01/vw/article/algebra/idas.html (359 words)

	Nokia and Wallpaper* Collaborate to Create Style-Centric Mobile Site
		We believe Wallpaper* to go will appeal to style-conscious Nokia mobile phone owners who like to keep an eye on the catwalks of London and Paris, the furniture shows in Milan, or ideas for that once-in-a-lifetime trip to the Seychelles.”
		Wallpaper* to go is available to any Nokia mobile phone user with GPRS connectivity.
		Wallpaper* magazine is the world's leading design authority.
	www.timewarner.com /corp/newsroom/pr/0,20812,1063881,00.html (507 words)

	The Geometry Junkyard: Symmetry and Group Theory
		The MSRI Computing Group uses another horoball diagram as their logo.
		ProtoZone interactive shockwave museum exhibits for exploring geometric concepts such as symmetry, tiling, and wallpaper groups.
		Group theoretic mathematics for determining whether a polygon formed out of hexagons can be dissected into three-hexagon triangles, or whether a polygon formed out of squares can be dissected into restricted-orientation triominoes.
	www.ics.uci.edu /~eppstein/junkyard/sym.html (1125 words)

	Sunlight Hotel Group - Desktop Wallpaper
		Establish which display properties your monitor is using, we have created these wallpapers for the following screen resolutions: 1280x1024, 1024x768 and 800x600.
		The wallpaper should appear as the new desktop.
		Note: Occasionally you will see that there are two versions of the wallpapers, one for Mac computers and one for Windows PC's.
	www.sunlighthoteles.com /wallpaper.shtml (223 words)

	Group theory of wallpaper patterns (Site not responding. Last check: 2007-10-10)
		Consider the set of all elements in the Euclidean group, E, such that the pattern on the result of the transformation is exactly the same pattern as the original.
		We denote this subset of E by G. We call G the wallpaper group of this pattern.
		Under this assumption, group G coincides with one of seventeen kinds seen on the previous page.
	mathmuse.sci.ibaraki.ac.jp /pattrn/Pattern2E.html (983 words)

	Wallpaper Groups (Site not responding. Last check: 2007-10-10)
		This group contains 60° rotations, that is, rotations of order 6.
		It also contains rotations of orders 2 and 3, but neither reflections nor glide reflections.
		A fundamental region for the symmetry group is one-sixth of an equilateral triangle of the lattice.
	www.clarku.edu /~djoyce/wallpaper/wall16.html (42 words)

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