<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-04898882</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-22T13:36:28+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">The E8 lattice and quasicrystals</title>
            <author role="aut">
              <persName>
                <forename type="first">J.F.</forename>
                <surname>Sadoc</surname>
              </persName>
              <email type="md5">ac53361ade6e1c0864728feef29e6087</email>
              <email type="domain">lps-u-sud.fr</email>
              <idno type="idhal" notation="numeric">1361994</idno>
              <idno type="halauthorid" notation="string">258602-1361994</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-3332-244X</idno>
              <affiliation ref="#struct-1208229"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">R.</forename>
                <surname>Mosseri</surname>
              </persName>
              <idno type="halauthorid">115978-0</idno>
            </author>
            <editor role="depositor">
              <persName>
                <forename>LPS</forename>
                <surname>Gestionnaire</surname>
              </persName>
              <email type="md5">892da8601da6d870e24ca8bf3ab08ad4</email>
              <email type="domain">u-psud.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2025-01-20 10:53:22</date>
              <date type="whenModified">2025-01-22 03:18:46</date>
              <date type="whenReleased">2025-01-20 10:53:22</date>
              <date type="whenProduced">1993</date>
              <ref type="externalLink" target="https://api.istex.fr/ark:/67375/6H6-TKLC7181-7/fulltext.pdf?sid=hal"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="1048593">
                <persName>
                  <forename>LPS</forename>
                  <surname>Gestionnaire</surname>
                </persName>
                <email type="md5">892da8601da6d870e24ca8bf3ab08ad4</email>
                <email type="domain">u-psud.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-04898882</idno>
            <idno type="halUri">https://hal.science/hal-04898882</idno>
            <idno type="halBibtex">sadoc:hal-04898882</idno>
            <idno type="halRefHtml">&lt;i&gt;Journal of Non-Crystalline Solids&lt;/i&gt;, 1993, 153-154 (C), pp.247-252. &lt;a target="_blank" href="https://dx.doi.org/10.1016/0022-3093(93)90351-W"&gt;&amp;#x27E8;10.1016/0022-3093(93)90351-W&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Journal of Non-Crystalline Solids, 1993, 153-154 (C), pp.247-252. &amp;#x27E8;10.1016/0022-3093(93)90351-W&amp;#x27E9;</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-PSUD">Université Paris Sud - Paris XI</idno>
            <idno type="stamp" n="UNIV-PARIS-SACLAY">Université Paris-Saclay</idno>
            <idno type="stamp" n="UNIV-PSUD-SACLAY" corresp="UNIV-PARIS-SACLAY">Université Paris Sud pour Paris Saclay</idno>
            <idno type="stamp" n="GS-PHYSIQUE">Graduate School Physique</idno>
            <idno type="stamp" n="LPSO">Laboratoire de Physique des Solides d'Orsay</idno>
            <idno type="stamp" n="URP-LPS">Laboratoire de Psychologie Sociale : contextes et régulation</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">The E8 lattice and quasicrystals</title>
                <author role="aut">
                  <persName>
                    <forename type="first">J.F.</forename>
                    <surname>Sadoc</surname>
                  </persName>
                  <email type="md5">ac53361ade6e1c0864728feef29e6087</email>
                  <email type="domain">lps-u-sud.fr</email>
                  <idno type="idhal" notation="numeric">1361994</idno>
                  <idno type="halauthorid" notation="string">258602-1361994</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-3332-244X</idno>
                  <affiliation ref="#struct-1208229"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">R.</forename>
                    <surname>Mosseri</surname>
                  </persName>
                  <idno type="halauthorid">115978-0</idno>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">15885</idno>
                <idno type="issn">0022-3093</idno>
                <title level="j">Journal of Non-Crystalline Solids</title>
                <imprint>
                  <publisher>Elsevier</publisher>
                  <biblScope unit="volume">153-154</biblScope>
                  <biblScope unit="issue">C</biblScope>
                  <biblScope unit="pp">247-252</biblScope>
                  <date type="datePub">1993</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1016/0022-3093(93)90351-W</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Fibonacci chains</term>
                <term xml:lang="en">Fibre selection</term>
                <term xml:lang="en">Hopf fibration</term>
                <term xml:lang="en">Quasicrystals</term>
                <term xml:lang="en">Shell by shell analysis</term>
                <term xml:lang="en">Crystals</term>
                <term xml:lang="en">E8 lattices</term>
                <term xml:lang="en">Cut and projection algorithms</term>
                <term xml:lang="en">Mathematical models</term>
                <term xml:lang="en">Crystal symmetry</term>
                <term xml:lang="en">Crystal lattices</term>
                <term xml:lang="en">Crystal atomic structure</term>
                <term xml:lang="en">Algorithms</term>
              </keywords>
              <classCode scheme="halDomain" n="phys">Physics [physics]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>In this paper we study the quasiperiodic structures that can be derived from the 8-dimensional lattice E8. We develop a modified version of the cut-and-projection algorithm. The high-dimensional lattice is first foliated into successive shells surrounding a vertex. The shells are embedded in 7-dimensional S7 sphers. We then use the so-called Hopf fibration of S7 to gather families of E8 shell sites into S3 fibres containing 24 sites (or multiples of 24) symmetrically disposed in S3. This selection process has two advantages: first, a whole fibre is either selected or rejected, which reduces the computation; more important, the fibre selection process is based on simple arithmetical criteria. The process leads to a shell-by-shell analysis of a 4D quasicrystal with {3, 3, 5} asymmetry, which can be brought onto a 2D-1D algorithm similar to the Fibonacci chain construction. We propose an arithmetic formula which gives the number of points on the successive shells. This 4D quasicrystal has the interesting feature that it can be sliced into lower-dimensional quasicrystals, for example with icosahedral and tetrahedral symmetry in 3 dimensions.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-1208229" status="OLD">
          <orgName>Laboratoire de Physique des Solides - MATRIX</orgName>
          <orgName type="acronym">LPS</orgName>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>Bat. 510 91405 Orsay cedex</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-134" type="direct"/>
            <relation active="#struct-92966" type="indirect"/>
            <relation name="UMR8502" active="#struct-441569" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-134" status="OLD">
          <orgName>Laboratoire de Physique des Solides</orgName>
          <orgName type="acronym">LPS</orgName>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>Bat. 510 91405 Orsay cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.lps.u-psud.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-92966" type="direct"/>
            <relation name="UMR8502" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-92966" status="OLD">
          <idno type="ROR">https://ror.org/028rypz17</idno>
          <orgName>Université Paris-Sud - Paris 11</orgName>
          <orgName type="acronym">UP11</orgName>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>Bâtiment 300 - 91405 Orsay cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.u-psud.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>