사용자토론:Kim Dongseok(KNU)
새 주제마지막 의견: 16년 전 (멀뚱이님) - 주제: 반스타 증정
Kim Dongseok(KNU)님, 한국어 위키백과에 오신 것을 환영합니다!
위키백과는 누구나 자유롭게 참여할 수 있는 ‘우리 모두의 백과사전’입니다.
각종 사용법과 규칙이 어려울 수 있지만, 차근차근 익히며 과감하게 기여하세요. 아래에 나열된 문서들이 위키백과 사용 및 편집에 도움을 줄 것입니다.
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길라잡이 위키백과에 대한 기본적인 길라잡이입니다. |
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사용자 모임 위키백과의 다양한 분야를 다루는 게시판 및 프로젝트가 모여 있습니다. |
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질문방 위키백과를 사용하는 방법이나 내용에 대해 질문합니다. |
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지원 단체 위키백과 커뮤니티를 지원하는 단체는? |
 
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--~~~~)를 입력하거나 편집 창에서 그림의 강조된 서명 버튼()을 누르면 됩니다.
Welcome! If you are not good at Korean or do not speak it, click here.
--Wybot 2007년 9월 29일 (토) 06:13 (KST)
그림 올리기에 관해서 장우영학생이 잘 설명하고 평면의 결정군의 토론에 보면 설명이 있습니다만 더 자세한 방법과 예시를 퇴프님이 보내주셔서 아래와 같이 올리니, 학생 여러분은 잘 지켜서 작성하여 주시기 바랍니다.
Public domain - old와 GFDL에 대해 예시삼아 공용에 각각 하나씩 올려봤습니다.
참고해주세요.
http://commons.wikimedia.org/wiki/Image:Wallpaper_group-p4m-5.jpg
http://commons.wikimedia.org/wiki/Image:Wallpaper_group-cell-pm.png
말씀하시는 학생이 언제, 어느 언어판에서 편집하였는지는 모르겠으나, 현재 한국어판에서는 저작권 지침이 공용과 완전히 일치하기 때문에 문서에 사용하 는 그림은 공용에 업로드하는것을 원칙으로 삼고 있습니다.
해당 토론:평면의 결정군 문서에서 문제가 되는 점은 다음과 같습니다.
인용: 설명란에 미국 위키백과에서 해당하는 그림파일에 대한 설명이 있을겁 니다. 이 부분을 번역하셔서 올려주시면 좋고 번역이 여의치 않은 경우 그냥 복사해서 내용을 채우시면 됩니다.
- 설명은 공용에서 정보 표에 맞게 써주셔야 합니다. 마이크로포맷을 이용한
정보 관리체계에 도움이 됩니다.
인용: 마지막에 인터위키라는 위키태그를 붙여주셔야 하는데요, 그냥 en:English Wikipedia 라고 써주시기만 하면 됩니다.
- 인터위키는 다른 위키프로젝트에 있는것과 연결시켜 주는 역할을 합니다.
한국어판에서는 en:그림이름와 같이 올려야 하며, 공용에서는 기본적으로 그림끼리의 연결에 인터위키를 사용하지 않습니다.
인용: 마지막으로 저작권 칸에는 이 그림이 GFDL 이라는 저작권 관련 협약을 준수하는 파일임을 입증하기 위해 저작권란에 'GFDL' 을 선택해주면 됩니다.
- 이 부분이 제일 위험합니다. Public Domain은 GFDL로 배포하는것은 법적으로
문제가 되지 않습니다. (관례상 비도덕적인것으로 여겨집니다.) 다른 라이선 스로 등록된 그림이 있는지 미처 확인해보지는 못했으나 위키백과에서 사용할 수 있는 것으로는 [크리에이티브 커먼즈]라는 저작권이 있는데, 이것은 GFDL 과 호환되지 않습니다. 또한 영어 위키백과에서 고유 채택하고 있는 [공정 사 용]은 한국어판과 공용에서는 인정되지 않습니다. 이것 또한 GFDL과 호환되지 않습니다.
인용:참고로 GFDL 이란 GNU Free Document Licence 의 줄임말로 GNU 자유문서 협약을 의미합니다. 리눅스와 같은 Open Source 진영에서 통용되는 규약입니다.
- 사소한 내용이지만, 이부분은 GFDL에 대해 잘못된 이해를 담고 있습니다. 어
떤 집단에서도 "통용되는" 라이선스 규약은 존재하지 않으며 GFDL은 단지 GPL 로 만들어진 소프트웨어의 설명서를 쓰기 위해 개발된 라이선스일 뿐입니다.
또한 문서의 토론란에는 문서의 내용 편집에 관한 토론을 하게 되는데, 해당 내용의 경우 문서를 편집하기 위한 내용이기는 하나 특정한 사용자를 위한 내 용으로서, 잘못된 공간 활용이라 할 수 있습니다. 다른 공간을 추천해드리고 싶은데, 마땅한 공간이 없네요.
하지만 다른 사용자의 지적이 들어온다면 그 사용자가 추천하는 곳으로 토론 공간을 적절한 곳으로 이동하면 좋겠습니다.
원래 편집자 개개인과 소통하는것이 맞는데, 평면의 결정군은 편집자가 너무 많아 어떤 식으로 해야 좋을지 모르겠습니다. (한 사용자에게 글을 쓰면 다른 사용자가 똑같은 편집을 하는 식입니다.)
--{{풀기:사:Kim Dongseok(KNU)/서명}} 2007년 10월 26일 (금) 21:29 (KST)
내용을 계속 붙이시는걸 보니 경북대학교 수학 작업을 주도하시는 분인듯 한데, 미번역 문서를 일반 공간에 두시면 안됩니다. 사용자문서에서 작업해주시면 좋겠습니다 :)
사용자:Kim Dongseok(KNU)나 사용자:Kim Dongseok(KNU)/평면의 결정군 같은 페이지를 만드시고 작업하신 후에 일반 공간으로 옮겨주시면 좋겠습니다. 고맙습니다. --퇴프 2007년 10월 25일 (목) 01:51 (KST)
| 미번역된 내용은 여기에 있습니다. | |
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==17개의 평면의 결정군의 설명==
===Group p1===
{{wallpaper_group_list|p1|o|The group '''p1''' contains only translations; there are no rotations, reflections, or glide reflections.}}
<gallery>
Image:WallpaperP1.GIF|<center>Computer generated</center>
Image:Wallpaper_group-p1-1.jpg|<center>[[Tomb]], [[Thebes (Egypt)|Thebes]], [[Ancient Egypt|Egypt]]. Easily confused with type '''p2'''.</center>
Image:Wallpaper_group-p1-2.jpg|<center>[[Persian empire|Persian]] [[tapestry]]</center>
Image:Wallpaper_group-p1-3.jpg|<center>[[Mediæval]] wall [[diapering]]</center>
</gallery>
The two translations (cell sides) can each have different lengths, and can form any angle.
===Group p2===
{{wallpaper_group_list|p2|2222|The group '''p2''' contains four rotation centres of order two (180°), but no reflections or glide reflections.}}
<gallery>
Image:WallpaperP2.GIF|<center>Computer generated</center>
Image:Wallpaper_group-p2-1.jpg|<center>Cloth, [[Sandwich Islands]] ([[Hawaii]])</center>
Image:Wallpaper_group-p2-2.jpg|<center>Mat on which [[Ancient Egypt|Egyptian]] king stood</center>
Image:Wallpaper_group-p2-2 detail 2.jpg|<center>Egyptian mat (detail)</center>
Image:Wallpaper_group-p2-3.jpg|<center>Ceiling of [[Ancient Egypt|Egyptian]] [[tomb]]</center>
Image:Wallpaper_group-p2-4.jpg|<center>Wire [[fence]], [[U.S.]]</center>
</gallery>
===Group pm===
{{wallpaper_group_list|pm|**|The group '''pm''' has no rotations. It has reflection axes, they are all parallel.}}
(The first three have a vertical symmetry axis, and the last two each have a different diagonal one.)
<gallery>
Image:WallpaperPM.GIF|<center>Computer generated</center>
Image:Wallpaper_group-pm-3.jpg|<center>Dress of a figure in a [[tomb]] at [[Biban el Moluk]], [[Ancient Egypt|Egypt]]</center>
Image:Wallpaper_group-pm-4.jpg|<center>[[Ancient Egypt|Egyptian]] [[tomb]], [[Thebes (Egypt)|Thebes]]</center>
Image:Wallpaper_group-pm-1.jpg|<center>Ceiling of a [[tomb]] at Gourna, [[Ancient Egypt|Egypt]]. Reflection axis is diagonal.</center>
Image:Wallpaper_group-pm-5.jpg|<center>[[India]]n metalwork at the [[Great Exhibition]] in 1851. The plane group is almost '''pm''' (ignoring short diagonal lines between ovals motifs).</center>
</gallery>
===Group pg===
{{wallpaper_group_list|pg|xx|The group '''pg''' contains glide reflections only, and their axes are all parallel. There are no rotations or reflections.}}
<gallery>
Image:WallpaperPG.GIF|<center>Computer generated</center>
Image:Wallpaper_group-pg-1.jpg|<center>Mat on which [[Ancient Egypt|Egyptian]] king stood</center>
Image:Wallpaper_group-pg-1 detail.jpg|<center>Egyptian mat (detail)</center>
Image:Wallpaper_group-pg-2.jpg|<center>Pavement in [[Salzburg]]. Glide reflection axis runs northeast-southwest.</center>
</gallery>
Without the details inside the zigzag bands the mat is [[#Group pmg|'''pmg''']]; with the details but without the distinction between brown and black it is [[#Group pgg|'''pgg''']].
Ignoring the wavy borders of the tiles, the pavement is [[#Group pgg|'''pgg''']].
{{-}}
===Group cm===
[[그림:Wallpaper_group-cell-cm.png|left|frame|Cell structure for '''cm''']]
[[그림:Wallpaper group diagram cm.svg|thumb|right|Cell structure for '''*x''']]
* Orbifold notation: '''*x'''.
* The group '''cm''' contains no rotations. It has reflection axes, all parallel. There is at least one glide reflection whose axis is ''not'' a reflection axis; it is halfway between two adjacent parallel reflection axes.
This groups applies for symmetrically staggered rows (i.e. there is a shift per row of half the translation distance inside the rows) of identical objects, which have a symmetry axis perpendicular to the rows.
<br style="clear:both;">
'''Examples of group ''cm'''''
<gallery>
Image:WallpaperCM.GIF|<center>Computer generated</center>
Image:Wallpaper_group-cm-1.jpg|<center>Dress of [[Amun]], from [[Abu Simbel]], [[Ancient Egypt|Egypt]]</center>
Image:Wallpaper_group-cm-2.jpg|<center>[[Dado (architecture)|Dado]] from [[Biban el Moluk]], [[Ancient Egypt|Egypt]]</center>
Image:Wallpaper_group-cm-3.jpg|<center>[[Bronze]] vessel in [[Nimroud]], [[Assyria]]</center>
Image:Wallpaper_group-cm-4.jpg|<center>[[Spandril]]s of [[arch|arches]], the [[Alhambra]], [[Spain]]</center>
Image:Wallpaper_group-cm-5.jpg|<center>[[Soffitt]] of arch, the [[Alhambra]], [[Spain]]</center>
Image:Wallpaper_group-cm-6.jpg|<center>[[Persian empire|Persian]] [[tapestry]]</center>
Image:Wallpaper_group-cm-7.jpg|<center>[[India]]n metalwork at the [[Great Exhibition]] in 1851</center>
Image:Wallpaper_group-pm-2.jpg|<center>Dress of a figure in a [[tomb]] at [[Biban el Moluk]], [[Ancient Egypt|Egypt]]</center>
</gallery>
===Group pmm===
{{wallpaper_group_list|pmm|*2222|The group '''pmm''' has reflections in two perpendicular directions, and four rotation centres of order two (180°) located at the intersections of the reflection axes.}}
<gallery>
Image:WallpaperPMM.GIF|<center>Computer generated</center>
Image:Wallpaper_group-pmm-1.jpg|<center>2D image of lattice [[fence]], [[U.S.]] (in 3D there is additional symmetry)</center>
Image:Wallpaper_group-pmm-2.jpg|<center>[[Mummy]] case stored in [[The Louvre]]</center>
Image:Wallpaper_group-pmm-3.jpg|<center>Ceiling of [[Ancient Egypt|Egyptian]] [[tomb]] (almost cmm)</center>
Image:Wallpaper_group-pmm-4.jpg|<center>[[Mummy]] case stored in [[The Louvre]]. Would be type '''p4''' except for the mismatched coloring.</center>
</gallery>
===Group pmg===
{{wallpaper_group_list|pmg|22*|The group '''pmg''' has two rotation centres of order two (180°), and reflections in only one direction. It has glide reflections whose axes are perpendicular to the reflection axes. The centres of rotation all lie on glide reflection axes.}}
<gallery>
Image:WallpaperPMG.GIF|<center>Computer generated</center>
Image:Wallpaper_group-pmg-1.jpg|<center>Cloth, [[Sandwich Islands]] ([[Hawaii]])</center>
Image:Wallpaper_group-pmg-2.jpg|<center>Ceiling of [[Ancient Egypt|Egyptian]] [[tomb]]</center>
Image:Wallpaper_group-pmg-3.jpg|<center>Floor tiling in [[Prague]], the [[Czech Republic]]</center>
Image:Wallpaper_group-pmg-4.jpg|<center>Bowl from [[Kingdom of Kerma|Kerma]]</center>
</gallery>
===Group pgg===
{{wallpaper_group_list|pgg|22x|The group '''pgg''' contains two rotation centres of order two (180°), and glide reflections in two perpendicular directions. The centres of rotation are not located on the glide reflection axes. There are no reflections.}}
<gallery>
Image:WallpaperPGG.GIF|<center>Computer generated</center>
Image:Wallpaper_group-pgg-1.jpg|<center>[[Bronze]] vessel in [[Nimroud]], [[Assyria]]</center>
Image:Wallpaper_group-pgg-2.jpg|<center>[[Pavement (roads)|Pavement]] in [[Budapest]], [[Hungary]]. Glide reflection axes are diagonal.</center>
</gallery>
===Group cmm===
[[그림:Wallpaper_group-cell-cmm.png|left|frame|Cell structure for '''cmm''']]
[[그림:Wallpaper group diagram cmm.svg|thumb|right|Cell structure for '''2*22''']]
* Orbifold notation: '''2*22'''.
* The group '''cmm''' has reflections in two perpendicular directions, and a rotation of order two (180°) whose centre is ''not'' on a reflection axis. It also has two rotations whose centres ''are'' on a reflection axis.
*This group is frequently seen in everyday life, since the most common arrangement of [[brick]]s in a brick building utilises this group (see example below).
The rotational symmetry of order 2 with centres of rotation at the centres of the sides of the rhombus is a consequence of the other properties.
The pattern corresponds to each of the following:
*symmetrically staggered rows of identical doubly symmetric objects
*a checkerboard pattern of two alternating rectangular tiles, of which each, by itself, is doubly symmetric
*a checkerboard pattern of alternatingly a 2-fold rotationally symmetric rectangular tile and its mirror image
<br style="clear:both;">
'''Examples of group ''cmm'''''
<gallery>
Image:WallpaperCMM.GIF|<center>Computer generated</center>
Image:Tile 33344.svg|<center>one of the 8 [[Tilings of regular polygons#Archimedean, uniform or semiregular tilings|semi-regular tessellations]]; ignoring color this is this group '''cmm''', otherwise group '''p1'''</center>
Image:Wallpaper_group-cmm-1.jpg|<center>Suburban [[brick]] wall, [[U.S.]]</center>
Image:Wallpaper_group-cmm-2.jpg|<center>Ceiling of [[Ancient Egypt|Egyptian]] [[tomb]]. It is group '''cmm''' if the colors are taken into account (they reduce the symmetry), otherwise it is [[#Group p4g|'''p4g''']].</center>
Image:Wallpaper_group-cmm-3.jpg|<center>[[Ancient Egypt|Egyptian]]</center>
Image:Wallpaper_group-cmm-4.jpg|<center>[[Persian empire|Persian]] [[tapestry]]</center>
Image:Wallpaper_group-cmm-5.jpg|<center>[[Ancient Egypt|Egyptian]] [[tomb]]</center>
Image:Wallpaper_group-cmm-6.jpg|<center>[[Turkic peoples|Turkish]] dish</center>
</gallery>
===Group p4===
{{wallpaper_group_list|p4|442|The group '''p4''' has two rotation centres of order four (90°), and one rotation centre of order two (180°). It has no reflections or glide reflections.}}
<gallery>
Image:WallpaperP4.GIF|<center>Computer generated</center>
Image:Tile 33434.svg|<center>one of the 8 [[Tilings of regular polygons#Archimedean, uniform or semiregular tilings|semi-regular tessellations]]</center>
Image:Wallpaper_group-p4-1.jpg|<center>Ceiling of [[Ancient Egypt|Egyptian]] [[tomb]]; ignoring colors this is '''p4''', otherwise [[#Group p2|'''p2''']]</center>
Image:Wallpaper_group-p4-2.jpg|<center>Ceiling of [[Ancient Egypt|Egyptian]] [[tomb]]</center>
Image:Wallpaper_group-p4-3.jpg|<center>Frieze, the [[Alhambra]], [[Spain]]. Requires close inspection to see why there are no reflections.</center>
Image:Wallpaper_group-p4-4.jpg|<center>Viennese cane</center>
Image:Wallpaper_group-p4-5.jpg|<center>Renaissance earthernware</center>
</gallery>
===Group p4m===
{{wallpaper_group_list|p4m|*442|The group '''p4m''' has two rotation centres of order four (90°), and reflections in four distinct directions (horizontal, vertical, and diagonals). It has additional glide reflections whose axes are not reflection axes; rotations of order two (180°) are centred at the intersection of the glide reflection axes. All rotation centres lie on reflection axes.
This corresponds to a straightforward grid of rows and columns of equal squares with the four reflection axes. Also it corresponds to a [[checkerboard]] pattern of two alternating squares.}}
Examples displayed with the smallest translations horizontal and vertical (like in the diagram):
<gallery>
Image:WallpaperP4M.GIF|<center>Computer generated</center>
Image:Tile 4,4.svg|<center>one of the 3 [[Tilings of regular polygons#Regular tilings|regular tessellations]] (in this checkerboard coloring, smallest translations are diagonal)</center>
Image:Tile V488.svg|<center>[[Tetrakis square tiling|Demiregular tiling with triangles]] (in this coloring, the smallest translations are orthogonal)</center>
Image:Tile 488.svg|<center>one of the 8 [[Tilings of regular polygons#Archimedean, uniform or semiregular tilings|semi-regular tessellations]] (ignoring color also, with smaller translations)</center>
Image:Wallpaper_group-p4m-1.jpg|<center>Ornamental painting, [[Nineveh]], [[Assyria]]</center>
Image:Wallpaper_group-p4m-3.jpg|<center>[[Storm drain]], [[U.S.]]</center>
Image:Wallpaper_group-p4m-5.jpg|<center>[[Ancient Egypt|Egyptian]] [[mummy]] case</center>
Image:Wallpaper_group-p4m-6.jpg|<center>[[Persian Empire|Persian]] [[glaze (painting technique)|glazed]] tile</center>
</gallery>
Examples displayed with the smallest translations diagonal (like on a checkerboard):
<gallery>
Image:Wallpaper_group-p4m-2.jpg|<center>Cloth, [[Otaheite]] ([[Tahiti]])
Image:Wallpaper_group-p4m-4.jpg|<center>[[Ancient Egypt|Egyptian]] [[tomb]]</center>
Image:Wallpaper_group-p4m-7.jpg|<center>Cathedral of [[Bourges]]</center>
Image:Wallpaper_group-p4m-8.jpg|<center>Dish from [[Turkey]], [[Ottoman Empire|Ottoman]] period</center>
</center>
</gallery>
===Group p4g===
{{wallpaper_group_list|p4g|4*2|The group '''p4g''' has two centres of rotation of order four (90°), which are each other's mirror image, but it has reflections in only two directions, which are perpendicular. There are rotations of order two (180°) whose centres are located at the intersections of reflection axes. It has glide reflections axes parallel to the reflection axes, in between them, and also at an angle of 45° with these.
In '''p4g''' there is a [[checkerboard]] pattern of 4-fold rotational tiles and their mirror image, or looking at it differently (by shifting half a tile) a checkerboard pattern of horizontally and vertically symmetric tiles and their 90° rotated version. Note that neither applies for a plain checkerboard pattern of black and white tiles, this is group [[#Group p4m|'''p4m''']] (with diagonal translation cells).
Note that the diagram on the left represents in area twice the smallest square that is repeated by translation.}}
<gallery>
Image:WallpaperP4G.GIF|<center>Computer generated</center>
Image:Wallpaper_group-p4g-1.jpg|<center>Bathroom [[linoleum]], [[U.S.]]</center>
Image:Wallpaper_group-p4g-2.jpg|<center>Painted [[porcelain]], [[China]]</center>
Image:Wallpaper_group-p4g-3.jpg|<center>Fly screen, [[U.S.]]</center>
Image:Wallpaper_group-p4g-4.jpg|<center>Painting, [[China]]</center>
</gallery>
===Group p3===
[[그림:Wallpaper_group-cell-p3.png|left|frame|Cell structure for '''p3''' (the rotation centres at the centres of the triangles are not shown)]]
[[그림:Wallpaper group diagram p3.svg|thumb|right|Cell structure for '''333''']]
* Orbifold notation: '''333'''.
* The group '''p3''' has three different rotation centres of order three (120°), but no reflections or glide reflections.
Imagine a tessellation of the plane with equilateral triangles of equal size, with the sides corresponding to the smallest translations. Then half of the triangles are in one orientation, and the other half upside down. 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, but the two are not equal, not each other's mirror image, and not both symmetric. For a given image, three of these tessellations are possible, each with rotation centres as vertices, i.e. for any tessellation two shifts are possible. In terms of the image: the vertices can be the red, the blue or the green triangles.
Equivalently, imagine a tessellation of the plane with hexagons of regular shape and equal size, with the sides corresponding to the smallest translations. Then this wallpaper group corresponds to the case that all hexagons are equal (and in the same orientation) and have rotational symmetry of order three, while they have no mirror image symmetry. For a given image, nine of these tessellations are possible, each with rotation centres as vertices. In terms of the image: the centres can be each of three selections of the red triangles, or of the blue or the green.
<br style="clear:both;">
'''Examples of group ''p3'''''
<gallery>
Image:WallpaperP3.GIF|<center>Computer generated</center>
Image:Tile 33336.svg|<center>one of the 8 [[Tilings of regular polygons#Archimedean, uniform or semiregular tilings|semi-regular tessellations]] (ignoring the colors: ''p6''); the translation vectors are rotated a little to the right compared with the directions in the underlying hexagonal lattice of the image</center>
Image:Wallpaper_group-p3-1.jpg|<center>Street pavement in [[Zakopane]], [[Poland]]</center>
Image:Alhambra-p3-closeup.jpg|<center>Wall tiling in the [[Alhambra]], [[Spain]] (and the [[:Image:Alhambra-p3-wall.jpg|whole wall]])</center>
</gallery>
===Group p3m1===
{{wallpaper_group_list|p3m1|*333|The group '''p3m1''' has three different rotation centres of order three (120°). It has reflections in the three sides of an equilateral triangle. The centre of every rotation lies on a reflection axis. There are additional glide reflections in three distinct directions, whose axes are located halfway between adjacent parallel reflection axes.
Like for [[#Group p3|'''p3''']], imagine a tessellation of the plane with equilateral triangles of equal size, with the sides corresponding to the smallest translations. Then half of the triangles are in one orientation, and the other half upside down. 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. For a given image, three of these tessellations are possible, each with rotation centres as vertices. In terms of the image: the vertices can be the red, the dark blue or the green triangles.
}}
<gallery>
Image:Tile 3,6.svg|<center>one of the 3 [[Tilings of regular polygons#Regular tilings|regular tessellations]] (ignoring colors: p6m)</center>
Image:Tile 6,3.svg|<center>another regular tessellation (ignoring colors: p6m)</center>
Image:Tile 3bb.svg|<center>one of the 8 [[Tilings of regular polygons#Archimedean, uniform or semiregular tilings|semi-regular tessellations]] (ignoring colors: p6m)</center>
Image:Wallpaper_group-p3m1-1.jpg|<center>[[Persian Empire|Persian]] [[glaze (painting technique)|glazed]] tile (ignoring colors: p6m)</center>
Image:Wallpaper_group-p3m1-3.jpg|<center>[[Persian Empire|Persian]] ornament</center>
Image:Wallpaper_group-p3m1-4.jpg|<center>Floor tiling in [[Budapest]], [[Hungary]] (ignoring colors: p6m)</center>
Image:Wallpaper_group-p3m1-2.jpg|<center>Painting, [[China]] (see detailed image)</center>
</gallery>
===Group p31m===
{{wallpaper_group_list|p31m|3*3|The group '''p31m''' has three different rotation centres of order three (120°), of which two are each other's mirror image. It has reflections in three distinct directions. It has at least one rotation whose centre does ''not'' lie on a reflection axis. There are additional glide reflections in three distinct directions, whose axes are located halfway between adjacent parallel reflection axes.
Like for '''p3''' and '''p3m1''', imagine a tessellation of the plane with equilateral triangles of equal size, with the sides corresponding to the smallest translations. Then half of the triangles are in one orientation, and the other half upside down. 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. For a given image, only one such tessellation is possible. In terms of the image: the vertices can ''not'' be dark blue triangles.
}}
<gallery>
Image:Wallpaper_group-p31m-1.jpg|<center>[[Persian empire|Persian]] [[glaze (painting technique)|glazed]] tile</center>
Image:Wallpaper_group-p31m-2.jpg|<center>Painted [[porcelain]], [[China]]</center>
Image:Wallpaper_group-p31m-3.jpg|<center>Painting, [[China]]</center>
</gallery>
===Group p6===
{{wallpaper_group_list|p6|632|The group '''p6''' has one rotation centre of order six (60°); it has also two rotation centres of order three, which only differ by a rotation of 60° (or, equivalently, 180°), and three of order two, which only differ by a rotation of 60°. It has no reflections or glide reflections.
}}
<gallery>
Image:WallpaperP6.GIF|<center>Computer generated</center>
Image:Wallpaper_group-p6-1.jpg|<center>Wall panelling, the [[Alhambra]], [[Spain]]</center>
Image:Wallpaper_group-p6-2.jpg|<center>[[Persian Empire|Persian]] ornament</center>
</gallery>
===Group p6m===
{{wallpaper_group_list|p6m|*632|The group '''p6m''' has one rotation centre of order six (60°); it has also two rotation centres of order three, which only differ by a rotation of 60° (or, equivalently, 180°), and three of order two, which only differ by a rotation of 60°. It has also reflections in six distinct directions. There are additional glide reflections in six distinct directions, whose axes are located halfway between adjacent parallel reflection axes.
|p6mm}}
<gallery>
Image:WallpaperP6M.GIF|<center>Computer generated</center>
Image:Tile 3636.svg|<center>one of the 8 [[Tilings of regular polygons#Archimedean, uniform or semiregular tilings|semi-regular tessellations]]</center>
Image:Tile 3464.svg|<center>another semi-regular tessellation</center>
Image:Tile 46b.svg|<center>another semi-regular tessellation</center>
Image:Wallpaper_group-p6m-1.jpg|<center>[[Persian empire|Persian]] [[glaze (painting technique)|glazed]] tile</center>
Image:Wallpaper_group-p6m-2.jpg|<center>King's dress, [[Khorsabad]], [[Assyria]]</center>
Image:Wallpaper_group-p6m-3.jpg|<center>[[Bronze]] vessel in [[Nimroud]], [[Assyria]]</center>
Image:Wallpaper_group-p6m-4.jpg|<center>[[Byzantine art|Byzantine]] [[marble]] pavement, [[Rome]]</center>
Image:Wallpaper_group-p6m-5.jpg|<center>Painted [[porcelain]], [[China]]</center>
Image:Wallpaper_group-p6m-6.jpg|<center>Painted [[porcelain]], [[China]]</center>
</gallery>
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통상적으로 지켜지는 관례를 무시한 편집은 다른 사용자에게 피해가 된다는 점을 유념해주셨으면 합니다. 그리고 틀은 용도에 맞게, 바르게 만들어주세요. --퇴프 2007년 10월 26일 (금) 21:29 (KST)
반스타 증정[편집]
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The Special Barnstar | |
| 수십명이 공동작업으로 편집하는 모습이 위키백과에서는 거의 최초인 듯 해서, 이 반스타를 드립니다. 대단한 교수님이십니다. ^^ |