A pentagonal crystal, the golden section, alcove packing and aperiodic tilings
Identifieur interne : 000607 ( Main/Exploration ); précédent : 000606; suivant : 000608A pentagonal crystal, the golden section, alcove packing and aperiodic tilings
Auteurs : Anthony Joseph [Israël]Source :
- Transformation Groups [ 1083-4362 ] ; 2009-09-01.
Abstract
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 A4. Similar crystals with (2n + 1)-fold symmetry are represented as Kashiwara crystals in type A2n . The weight diagrams of the latter inspire higher aperiodic tiling. In another approach alcove packing is seen to give aperiodic tiling in type A4. Finally 2m-fold symmetry is related to type B m .
Url:
DOI: 10.1007/s00031-009-9064-y
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 001024
- to stream Istex, to step Curation: 001024
- to stream Istex, to step Checkpoint: 000562
- to stream Main, to step Merge: 000611
- to stream Main, to step Curation: 000607
Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">A pentagonal crystal, the golden section, alcove packing and aperiodic tilings</title>
<author><name sortKey="Joseph, Anthony" sort="Joseph, Anthony" uniqKey="Joseph A" first="Anthony" last="Joseph">Anthony Joseph</name>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:4FA17D1DA83DC2B73FB07DF24821396178CE7CCB</idno>
<date when="2009" year="2009">2009</date>
<idno type="doi">10.1007/s00031-009-9064-y</idno>
<idno type="url">https://api.istex.fr/document/4FA17D1DA83DC2B73FB07DF24821396178CE7CCB/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">001024</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001024</idno>
<idno type="wicri:Area/Istex/Curation">001024</idno>
<idno type="wicri:Area/Istex/Checkpoint">000562</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000562</idno>
<idno type="wicri:doubleKey">1083-4362:2009:Joseph A:a:pentagonal:crystal</idno>
<idno type="wicri:Area/Main/Merge">000611</idno>
<idno type="wicri:Area/Main/Curation">000607</idno>
<idno type="wicri:Area/Main/Exploration">000607</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">A pentagonal crystal, the golden section, alcove packing and aperiodic tilings</title>
<author><name sortKey="Joseph, Anthony" sort="Joseph, Anthony" uniqKey="Joseph A" first="Anthony" last="Joseph">Anthony Joseph</name>
<affiliation wicri:level="1"><country xml:lang="fr">Israël</country>
<wicri:regionArea>Department of Mathematics, The Weizmann Institute of Science, 76100, Rehovot</wicri:regionArea>
<wicri:noRegion>Rehovot</wicri:noRegion>
</affiliation>
<affiliation wicri:level="1"><country wicri:rule="url">Israël</country>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series><title level="j">Transformation Groups</title>
<title level="j" type="abbrev">Transformation Groups</title>
<idno type="ISSN">1083-4362</idno>
<idno type="eISSN">1531-586X</idno>
<imprint><publisher>SP Birkhäuser Verlag Boston</publisher>
<pubPlace>Boston</pubPlace>
<date type="published" when="2009-09-01">2009-09-01</date>
<biblScope unit="volume">14</biblScope>
<biblScope unit="issue">3</biblScope>
<biblScope unit="page" from="557">557</biblScope>
<biblScope unit="page" to="612">612</biblScope>
</imprint>
<idno type="ISSN">1083-4362</idno>
</series>
</biblStruct>
</sourceDesc>
<seriesStmt><idno type="ISSN">1083-4362</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass></textClass>
<langUsage><language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">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 A4. Similar crystals with (2n + 1)-fold symmetry are represented as Kashiwara crystals in type A2n . The weight diagrams of the latter inspire higher aperiodic tiling. In another approach alcove packing is seen to give aperiodic tiling in type A4. Finally 2m-fold symmetry is related to type B m .</div>
</front>
</TEI>
<affiliations><list><country><li>Israël</li>
</country>
</list>
<tree><country name="Israël"><noRegion><name sortKey="Joseph, Anthony" sort="Joseph, Anthony" uniqKey="Joseph A" first="Anthony" last="Joseph">Anthony Joseph</name>
</noRegion>
<name sortKey="Joseph, Anthony" sort="Joseph, Anthony" uniqKey="Joseph A" first="Anthony" last="Joseph">Anthony Joseph</name>
</country>
</tree>
</affiliations>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000607 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000607 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Mathematiques |area= BourbakiV1 |flux= Main |étape= Exploration |type= RBID |clé= ISTEX:4FA17D1DA83DC2B73FB07DF24821396178CE7CCB |texte= A pentagonal crystal, the golden section, alcove packing and aperiodic tilings }}
This area was generated with Dilib version V0.6.33. |