A pentagonal crystal, the golden section, alcove packing and aperiodic tilings
Abstract A Lie theoretic interpretation is given to a pattern with five-fold symmetry occurring in aperiodic Penrose tiling based on isosceles triangles with length ratios equal to the Golden Section. Specifically a B(∞) crystal based on that of Kashiwara is constructed exhibiting this five-fold sym...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Joseph, Anthony [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2009 |
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| Schlagwörter: |
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| Anmerkung: |
© Birkhäuser Boston 2009 |
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| Übergeordnetes Werk: |
Enthalten in: Transformation groups - Boston, Mass. : Birkhäuser, 1996, 14(2009), 3 vom: 31. Juli, Seite 557-612 |
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| Übergeordnetes Werk: |
volume:14 ; year:2009 ; number:3 ; day:31 ; month:07 ; pages:557-612 |
| Links: |
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| DOI / URN: |
10.1007/s00031-009-9064-y |
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| Katalog-ID: |
SPR000320463 |
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| 100 | 1 | |a Joseph, Anthony |e verfasserin |4 aut | |
| 245 | 1 | 2 | |a A pentagonal crystal, the golden section, alcove packing and aperiodic tilings |
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| 520 | |a Abstract A Lie theoretic interpretation is given to a pattern with five-fold symmetry occurring in aperiodic Penrose tiling based on isosceles triangles with length ratios equal to the Golden Section. Specifically a B(∞) crystal based on that of Kashiwara is constructed exhibiting this five-fold symmetry. It is shown that it can be represented as a Kashiwara B(∞) crystal in type $ A_{4} $. Similar crystals with (2n + 1)-fold symmetry are represented as Kashiwara crystals in type $ A_{2n} $. The weight diagrams of the latter inspire higher aperiodic tiling. In another approach alcove packing is seen to give aperiodic tiling in type $ A_{4} $. Finally 2m-fold symmetry is related to type $ B_{m} $. | ||
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| 650 | 4 | |a Isosceles Triangle |7 (dpeaa)DE-He213 | |
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10.1007/s00031-009-9064-y doi (DE-627)SPR000320463 (SPR)s00031-009-9064-y-e DE-627 ger DE-627 rakwb eng Joseph, Anthony verfasserin aut A pentagonal crystal, the golden section, alcove packing and aperiodic tilings 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Birkhäuser Boston 2009 Abstract A Lie theoretic interpretation is given to a pattern with five-fold symmetry occurring in aperiodic Penrose tiling based on isosceles triangles with length ratios equal to the Golden Section. Specifically a B(∞) crystal based on that of Kashiwara is constructed exhibiting this five-fold symmetry. It is shown that it can be represented as a Kashiwara B(∞) crystal in type $ A_{4} $. Similar crystals with (2n + 1)-fold symmetry are represented as Kashiwara crystals in type $ A_{2n} $. The weight diagrams of the latter inspire higher aperiodic tiling. In another approach alcove packing is seen to give aperiodic tiling in type $ A_{4} $. Finally 2m-fold symmetry is related to type $ B_{m} $. Weyl Group (dpeaa)DE-He213 Simple Root (dpeaa)DE-He213 Chebyshev Polynomial (dpeaa)DE-He213 Coxeter Group (dpeaa)DE-He213 Isosceles Triangle (dpeaa)DE-He213 Enthalten in Transformation groups Boston, Mass. : Birkhäuser, 1996 14(2009), 3 vom: 31. Juli, Seite 557-612 (DE-627)346828589 (DE-600)2077379-1 1531-586X nnns volume:14 year:2009 number:3 day:31 month:07 pages:557-612 https://dx.doi.org/10.1007/s00031-009-9064-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 14 2009 3 31 07 557-612 |
| spelling |
10.1007/s00031-009-9064-y doi (DE-627)SPR000320463 (SPR)s00031-009-9064-y-e DE-627 ger DE-627 rakwb eng Joseph, Anthony verfasserin aut A pentagonal crystal, the golden section, alcove packing and aperiodic tilings 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Birkhäuser Boston 2009 Abstract A Lie theoretic interpretation is given to a pattern with five-fold symmetry occurring in aperiodic Penrose tiling based on isosceles triangles with length ratios equal to the Golden Section. Specifically a B(∞) crystal based on that of Kashiwara is constructed exhibiting this five-fold symmetry. It is shown that it can be represented as a Kashiwara B(∞) crystal in type $ A_{4} $. Similar crystals with (2n + 1)-fold symmetry are represented as Kashiwara crystals in type $ A_{2n} $. The weight diagrams of the latter inspire higher aperiodic tiling. In another approach alcove packing is seen to give aperiodic tiling in type $ A_{4} $. Finally 2m-fold symmetry is related to type $ B_{m} $. Weyl Group (dpeaa)DE-He213 Simple Root (dpeaa)DE-He213 Chebyshev Polynomial (dpeaa)DE-He213 Coxeter Group (dpeaa)DE-He213 Isosceles Triangle (dpeaa)DE-He213 Enthalten in Transformation groups Boston, Mass. : Birkhäuser, 1996 14(2009), 3 vom: 31. Juli, Seite 557-612 (DE-627)346828589 (DE-600)2077379-1 1531-586X nnns volume:14 year:2009 number:3 day:31 month:07 pages:557-612 https://dx.doi.org/10.1007/s00031-009-9064-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 14 2009 3 31 07 557-612 |
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10.1007/s00031-009-9064-y doi (DE-627)SPR000320463 (SPR)s00031-009-9064-y-e DE-627 ger DE-627 rakwb eng Joseph, Anthony verfasserin aut A pentagonal crystal, the golden section, alcove packing and aperiodic tilings 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Birkhäuser Boston 2009 Abstract A Lie theoretic interpretation is given to a pattern with five-fold symmetry occurring in aperiodic Penrose tiling based on isosceles triangles with length ratios equal to the Golden Section. Specifically a B(∞) crystal based on that of Kashiwara is constructed exhibiting this five-fold symmetry. It is shown that it can be represented as a Kashiwara B(∞) crystal in type $ A_{4} $. Similar crystals with (2n + 1)-fold symmetry are represented as Kashiwara crystals in type $ A_{2n} $. The weight diagrams of the latter inspire higher aperiodic tiling. In another approach alcove packing is seen to give aperiodic tiling in type $ A_{4} $. Finally 2m-fold symmetry is related to type $ B_{m} $. Weyl Group (dpeaa)DE-He213 Simple Root (dpeaa)DE-He213 Chebyshev Polynomial (dpeaa)DE-He213 Coxeter Group (dpeaa)DE-He213 Isosceles Triangle (dpeaa)DE-He213 Enthalten in Transformation groups Boston, Mass. : Birkhäuser, 1996 14(2009), 3 vom: 31. Juli, Seite 557-612 (DE-627)346828589 (DE-600)2077379-1 1531-586X nnns volume:14 year:2009 number:3 day:31 month:07 pages:557-612 https://dx.doi.org/10.1007/s00031-009-9064-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 14 2009 3 31 07 557-612 |
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10.1007/s00031-009-9064-y doi (DE-627)SPR000320463 (SPR)s00031-009-9064-y-e DE-627 ger DE-627 rakwb eng Joseph, Anthony verfasserin aut A pentagonal crystal, the golden section, alcove packing and aperiodic tilings 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Birkhäuser Boston 2009 Abstract A Lie theoretic interpretation is given to a pattern with five-fold symmetry occurring in aperiodic Penrose tiling based on isosceles triangles with length ratios equal to the Golden Section. Specifically a B(∞) crystal based on that of Kashiwara is constructed exhibiting this five-fold symmetry. It is shown that it can be represented as a Kashiwara B(∞) crystal in type $ A_{4} $. Similar crystals with (2n + 1)-fold symmetry are represented as Kashiwara crystals in type $ A_{2n} $. The weight diagrams of the latter inspire higher aperiodic tiling. In another approach alcove packing is seen to give aperiodic tiling in type $ A_{4} $. Finally 2m-fold symmetry is related to type $ B_{m} $. Weyl Group (dpeaa)DE-He213 Simple Root (dpeaa)DE-He213 Chebyshev Polynomial (dpeaa)DE-He213 Coxeter Group (dpeaa)DE-He213 Isosceles Triangle (dpeaa)DE-He213 Enthalten in Transformation groups Boston, Mass. : Birkhäuser, 1996 14(2009), 3 vom: 31. Juli, Seite 557-612 (DE-627)346828589 (DE-600)2077379-1 1531-586X nnns volume:14 year:2009 number:3 day:31 month:07 pages:557-612 https://dx.doi.org/10.1007/s00031-009-9064-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 14 2009 3 31 07 557-612 |
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10.1007/s00031-009-9064-y doi (DE-627)SPR000320463 (SPR)s00031-009-9064-y-e DE-627 ger DE-627 rakwb eng Joseph, Anthony verfasserin aut A pentagonal crystal, the golden section, alcove packing and aperiodic tilings 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Birkhäuser Boston 2009 Abstract A Lie theoretic interpretation is given to a pattern with five-fold symmetry occurring in aperiodic Penrose tiling based on isosceles triangles with length ratios equal to the Golden Section. Specifically a B(∞) crystal based on that of Kashiwara is constructed exhibiting this five-fold symmetry. It is shown that it can be represented as a Kashiwara B(∞) crystal in type $ A_{4} $. Similar crystals with (2n + 1)-fold symmetry are represented as Kashiwara crystals in type $ A_{2n} $. The weight diagrams of the latter inspire higher aperiodic tiling. In another approach alcove packing is seen to give aperiodic tiling in type $ A_{4} $. Finally 2m-fold symmetry is related to type $ B_{m} $. Weyl Group (dpeaa)DE-He213 Simple Root (dpeaa)DE-He213 Chebyshev Polynomial (dpeaa)DE-He213 Coxeter Group (dpeaa)DE-He213 Isosceles Triangle (dpeaa)DE-He213 Enthalten in Transformation groups Boston, Mass. : Birkhäuser, 1996 14(2009), 3 vom: 31. Juli, Seite 557-612 (DE-627)346828589 (DE-600)2077379-1 1531-586X nnns volume:14 year:2009 number:3 day:31 month:07 pages:557-612 https://dx.doi.org/10.1007/s00031-009-9064-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 14 2009 3 31 07 557-612 |
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English |
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Enthalten in Transformation groups 14(2009), 3 vom: 31. Juli, Seite 557-612 volume:14 year:2009 number:3 day:31 month:07 pages:557-612 |
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Enthalten in Transformation groups 14(2009), 3 vom: 31. Juli, Seite 557-612 volume:14 year:2009 number:3 day:31 month:07 pages:557-612 |
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Weyl Group Simple Root Chebyshev Polynomial Coxeter Group Isosceles Triangle |
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Joseph, Anthony @@aut@@ |
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2009-07-31T00:00:00Z |
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Joseph, Anthony misc Weyl Group misc Simple Root misc Chebyshev Polynomial misc Coxeter Group misc Isosceles Triangle A pentagonal crystal, the golden section, alcove packing and aperiodic tilings |
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A pentagonal crystal, the golden section, alcove packing and aperiodic tilings Weyl Group (dpeaa)DE-He213 Simple Root (dpeaa)DE-He213 Chebyshev Polynomial (dpeaa)DE-He213 Coxeter Group (dpeaa)DE-He213 Isosceles Triangle (dpeaa)DE-He213 |
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pentagonal crystal, the golden section, alcove packing and aperiodic tilings |
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A pentagonal crystal, the golden section, alcove packing and aperiodic tilings |
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Abstract A Lie theoretic interpretation is given to a pattern with five-fold symmetry occurring in aperiodic Penrose tiling based on isosceles triangles with length ratios equal to the Golden Section. Specifically a B(∞) crystal based on that of Kashiwara is constructed exhibiting this five-fold symmetry. It is shown that it can be represented as a Kashiwara B(∞) crystal in type $ A_{4} $. Similar crystals with (2n + 1)-fold symmetry are represented as Kashiwara crystals in type $ A_{2n} $. The weight diagrams of the latter inspire higher aperiodic tiling. In another approach alcove packing is seen to give aperiodic tiling in type $ A_{4} $. Finally 2m-fold symmetry is related to type $ B_{m} $. © Birkhäuser Boston 2009 |
| abstractGer |
Abstract A Lie theoretic interpretation is given to a pattern with five-fold symmetry occurring in aperiodic Penrose tiling based on isosceles triangles with length ratios equal to the Golden Section. Specifically a B(∞) crystal based on that of Kashiwara is constructed exhibiting this five-fold symmetry. It is shown that it can be represented as a Kashiwara B(∞) crystal in type $ A_{4} $. Similar crystals with (2n + 1)-fold symmetry are represented as Kashiwara crystals in type $ A_{2n} $. The weight diagrams of the latter inspire higher aperiodic tiling. In another approach alcove packing is seen to give aperiodic tiling in type $ A_{4} $. Finally 2m-fold symmetry is related to type $ B_{m} $. © Birkhäuser Boston 2009 |
| abstract_unstemmed |
Abstract A Lie theoretic interpretation is given to a pattern with five-fold symmetry occurring in aperiodic Penrose tiling based on isosceles triangles with length ratios equal to the Golden Section. Specifically a B(∞) crystal based on that of Kashiwara is constructed exhibiting this five-fold symmetry. It is shown that it can be represented as a Kashiwara B(∞) crystal in type $ A_{4} $. Similar crystals with (2n + 1)-fold symmetry are represented as Kashiwara crystals in type $ A_{2n} $. The weight diagrams of the latter inspire higher aperiodic tiling. In another approach alcove packing is seen to give aperiodic tiling in type $ A_{4} $. Finally 2m-fold symmetry is related to type $ B_{m} $. © Birkhäuser Boston 2009 |
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Specifically a B(∞) crystal based on that of Kashiwara is constructed exhibiting this five-fold symmetry. It is shown that it can be represented as a Kashiwara B(∞) crystal in type $ A_{4} $. Similar crystals with (2n + 1)-fold symmetry are represented as Kashiwara crystals in type $ A_{2n} $. The weight diagrams of the latter inspire higher aperiodic tiling. In another approach alcove packing is seen to give aperiodic tiling in type $ A_{4} $. 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