Wallpaper group diagrams
Jump to navigation
Jump to search
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. Such patterns occur frequently in architecture and decorative art. There are 17 possible distinct groups.
Overview of wallpaper groups
[edit]The region shown is a choice of the possible translation cells with minimum area, except for cm and cmm, where a region of twice that area is shown. The yellow region is a fundamental domain.
Files used to generate wallpaper group images
[edit]To avoid confusing any parts of MediaWiki or your browser, I encoded the files in gziped base64.
XML description of all wallpaper groups
[edit]begin-base64 644 Wallpaper_group_diagrams.xml.gz H4sICDhVEEkAA1dhbGxwYXBlcl9ncm91cF9kaWFncmFtcy54bWwA7Vvbcpsw EH3PVzD02TYImZoZJ/9CEuPJjIkzucy0f19hIZC0u5LAmLit81ADu+iy2j3n SHa3+/fj19vHw91dFG1P19FrWe/u47e8jqPy132cJeLz930sPh7FbboWn+KW 5XH0vHs91uIRix/E66KB3ZO8EJdve3XZ3ESlbKD5d2UbcsrATwbeG7arvtlt 3biIvuXL0bu42WiNbF/0ThszYWyaENbcbU4ZsBt9L+D7pp1uQPXQj367UpHc vh8/o6fj1+unCHncRxeNmx7n3H6c44/bMRDuwtoNSYwEjimzxgSX7PR4c3q8 8TSWx9hMiAn2Q7OmAvz7MGPd7yrR/eEoFuBHVRXiTxvEwc5I2IU3u+Fo/Y2B ETsnv1LjFPPaVci8mllVVT+vQ1SmsiX5UbK2S2aHFQSArFXvNHNsxGgfIIH9 AbOzlYrK/vDcRSURf+7VztyTRUYIx2GNvRgYhWwAXMJAK0vhCE+XD4WRDxmS DkbeFGbeZH1xiSAj4S6KJuBauAFBkBPzRhWZMkTBjju6EYqLhvEw8puY+wAs emGDznU3K77oLgRx6WaMlxRa47SoWxHW0803Spud0uicztLZFB2Z7sh8gKQL kGyE0Su4AhUd7WA04MltgaDirvzcyToweEdn4/OTzM7Ym24ar5s68ro2ioL1 XKfzshQ2OytBffWM8IVORk7jCCKT9jQn6z0nGiAr2irirsI3ibugycrVWqyq JOlb5HaLoViglaWluGbEBlwz/m97DUfHt73FOXsLh8q5QkwMVD83xPs7EY9O Rr6X2fhzY2RjIpOxedomIw/KRTkCJOM86ooRCXei54V8eSE1bQEyRnWK8rNu XLjfRQ5ndXPhyUR7p0isEpyw5g3kNTe9iQTjQxKK6AN4E4KfOUaksaq2iBeL hqlHcV4zUDuVqM1bdKfAPTPcMuCWmlpBunHglmGUoqFP2CkUJk841WXrxg23 BHTpwIP6KvBg/Pb7BgYcsE3PX+sZgMI/rJZWh+DKoG8KyPLghlsCKhL/cgIc HoQfM4FAekUbjDEKcWZImhHaIWHGXJkHMZgROYaFBD93mAvd/ch1bcAVpnBu oPUvghaZpk91S7CFuf3j65GJ6jnhRgwgtc844PacliH5SOweqYQkN3eD9lDT JgUbkKsuViPmaW45F0SToVUJQRUr1ouwbbbcSMdFslT8smyJqHli+0u3R/Vm 2brJ1pcoJ7loOoTy9b6VXF9mqu9Wsp9scHI/W62t/Lnyb0w4f3pEPsPGCuPE MJGvhQffV9g/JsDon1QJDFtx2CXNzvv2nCHN1pPwM8h2Mt/psvEcNBDARxi5 y6i/SWJi8G+sSEwscHqahcAhKF4enwNANnhnfd7RwLCim/b8gC66eq6iI0UI qZanESHOWkyCJMiAcnPkdYrndYYnMPDmpneISgiqfNARc3Tk+UrMPkwiKMTm BtuN46JhGFGaIyNJnWMT8B7A4TXr3k6HFGM9bTHOtkOd8MxtomqbW+X7NXmY +A6jTr2uQ8W/S86fAyBTHseRyBEACbbO93U5GhKGbC3Cj87OPa3r2nKcK3z3 sULAf4UYc6yg40QYQ6Gbu1RtLAu1uVOyawm13snrsXuxbN3ajWuKrTD8ysm9 ZSKSaASvXETjDZdy5O8PnBmh3g3/JaWWDzZp5/mFcMjQCQNBwK8LZlo/T+GS qj5AFoxcv3MV5wjeGA3i9Pqxdv0SE3mzuZF38AL6f618gY3STbp9n3Sjczi9 khweTCJ+nOkn3V59PNz9AWU0IDBTOgAA ====
XSLT to build SVG images from above XML file
[edit]begin-base64 644 Wallpaper_group_diagrams.xsl.gz H4sIAHQ3AkQAA+1a227bNhi+rp+CUIzFSS3LcpIiTus0azsUBdphWIt1Q9AL WqJlopIoUHRsIciT7WKPtFfYT+pgypYUy0iwFqjbxBbJ//TxP5HOv3//8+Ll KvDRDeExZeHEsAdDA5HQYS4NvYmxEDPz3Hh52Xmxiv2LWCQ+ieeEiA5CQBbG FzA8MeZCRBeWtVwuB8uTAeOeZY/HY+vPj++tTxyH8YzxwFiT+DT8WkukZovF VctGw+HQim88uaik92UHRjJFOY3MOMIOQcQnAQkFsDo2rPUSthDRQqCAiDlz JwZIM1AscOhin4VkYoTMQDR0gXJiJCSWwhBymSOSiJjRYupTZ2KYlvX55LVl vfn0Bn384y2yB7Zl/fKrgUqr4yQWJKgy5S3H0Zw6sQXEliQGRtI02x64wtXV BQaRjwVBARbOfGJ4nC2iGEyWgtQKHEV+YubrYhSD4Y7IVl5fhTggk678/UXy BSJL53uPJF3QDeYUT32CFEtjSV0xNwpxZ0P0FF0Bbiw47l3h1dOr6eoolVhN PyfUm4taBgkwSBoZCOqTTL/ChJW4HPZzC+FBn73B/oKYbFZIrBOmc0MtmYHl VWza6gTqPIQ2WxtR0mnY2rjpwxiHC+NSynxjszEIBD3AbSNjqjxuYoxsJzBQ 6j4wP3KCfMENJctXbAXxOTpD8ue2q2ju4EO6/i5fGnESE35Dfo4jUO13LCiD ZPCBhn/BD2QHIsqu5bBAZpPLzhNtNz7TrzQgLsXo1cJDB6cn5+cXSFDhk588 8fwz9v0IR4QjFUolsJ/UACQ9ew2xDvJPvnhuKd5Vu2aVdMwGXRI7Vaw6n+Y0 RvBfzAnkPr5wxIITBHZ4HAcI9JETS1yrfYllGyM6nXd9xdzhBAvGU1mgyZLx r33YU06mCeLACMcEUQGZWDBFkGZeSK0BpuEgtUBmPkoUse/CRpMB8A+RI2lF ZmLIBPKJB1uRoIjFMQU366N3YBQOBcJhAklfCeDSPTogbZFTS50QlDC5CuRz IAfSJYXCsVCkyGGhS8FzwnjQqdoUfQNeOD6NfsNijqi7kbtgMmJ+4rEQVKSq ZN125Yo7LdqsnL4Y8eTesa+QCQ+G6mVkA2YWKCcGmlHflzUtlNKeNNYL4khp zWs8371/ESezHRYxoRvn5ekAYr9NkQKlM0oNjbF65cYfOOplIAmgGWGJzIL7 vQOJ8FE5yuu0pZquXs53Bq/h0Njw8zoWkXdtf6k0uaXBVuQ1VGUoP4VIHDok hii7uFAhbGm1qZI0aSJNmkinTVKnjVKnTVKnjVJVNWmgTucbGDirvBzkPHrx IuhJc4+Ou1A6s6cpPEERhQx5AzG/CEUvauxMnGSLbxd6jC70GMddpRUyUUlU UhKVNIhyIJUV7pXJA4/Il0j/3s4LWhrIFIMc9AGqorOStdFJ7hCoNBoie4h8 dDpE8p98hlE7G5Vv7TpI2uCnkb1b5A0GloocK9LCp7JrqBIy2ijiVdi1ZcrX HnfFC2IPifzEA9ldfpQyerfdaHR3hCDbpU8cHmJQg/RMu2/aR6i01N6YbQHR 2gpPUx3UMQl25vraoMx1M6Y281kVZq6ex7ZRaweHPutqk1clrHaGqg1YpTSs 47WTl2fuwITu5hGWLVSWBpjPeCl49dm01NdOz5jvliaz82w27W34hoCT73RR aCUDfmsn5ww6mPVgNryckxABRNKfU431JbVNXsk43Rckvy0hDFosvqRl8XW8 u7W8K9hkrW/JtnSswGSjIdY6+NcAKOG9+Eg2ojv05918V/RTgHJYaALv7QC1 FmWmXpsN2/g+Lw6YqzxHNYvG9lZCb2pW+Nha/7LTaViVBW2Fh9T+W9UtXZWF R5v6BBt3faWK7OTZFz2Iq3LeOs7rDFK+UZhzGNOVHDncODFvkaXOvqZTRXs2 u5cug6sAq2Bg2udwtDfHkBbPBs9Q9t5HanjcV4Nm+n5YLn4lu/dE8vThkZyx Bd8XStmi7wqlDuGZRA3Jd3grfsPzI0B28vCQiTknZD/MJGL7YXbet4eDU5S/ D/vQQQ7OHwGw0SMAtmT7w7V7tK4JFTrQUkNMDvvwyZQfHwwrMrtOK3SB1DqR b1XB9zQkWQ0EQqlfm2q2a/Ha7rkqmJwaRY28TQ24a8225YlaYhUy0UvFHX2/ gKl7D2gqHhkvz3e3fGt703I1XRzPMec4mRgyi66vSxpR9XzqkjbY1hu6h3WV 3qAfqsdj7bLte7MwMipbtV3OJ+UjyGarV3kQybhs+OR2Y73Z/NW18FUyiqPm phgF5/rYWHuF3XgvUOZ2VMuEzrJTFBwxr9JD7HYXrJ0YqvWpA0hjalVzrdbM SlVrhHXvBjryjUbv8GlI9nGPmo6/mN+qrjGJtNKKDlscIh4Ej+IarkDGa0Zm z7ipvVze4bz1bWDk6rj8uLtudXe9eQWD5R21/NJ8Kq+nS4urv5et5mMixSlB Zsop2fGWN8+T68JSU0nKnnfYuI8/XOD/cIH0SwnlBE9R/jBVHlHlGrVs5E63 +orA/+Ezj+gzsv6ilS3bcmwXnmJLVyn+ECKR0037bxcOIAmTgnA1UnxHBd9R me/oHr6jgu8o5VvlOAh1sm/W13+Ddtn5D7Kjvw+/JgAA ====
See also
[edit] The article Wallpaper group diagrams on Wikipedia projects:
- (en) Wallpaper group
- (de) Ebene kristallographische Gruppe
- (nl) Behangpatroongroep