@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr:-LR1BQFJ7-F
  skos:broader psr:-XPFQM0ZH-H, psr:-WVB8LP7M-L ;
  dc:created "2023-07-28"^^xsd:date ;
  skos:definition """En géométrie, un <b>diagramme de Schlegel</b> est une projection d'un polytope de l'espace à <i>d</i> dimensions <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle R^{d}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msup>
<br/>          <mi>R</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>d</mi>
<br/>          </mrow>
<br/>        </msup>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle R^{d}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c2fc383f28fee81277353c81fb7ede49303ebc3" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:2.856ex; height:2.676ex;" alt="R^{d}"></span> dans l'espace à <i>d-1</i> dimensions <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle R^{d-1}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msup>
<br/>          <mi>R</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>d</mi>
<br/>            <mo>−<!-- − --></mo>
<br/>            <mn>1</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle R^{d-1}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a1ace73ab45be2e58aaf709e7436c96ad4095ace" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:4.957ex; height:2.676ex;" alt="{\\\\displaystyle R^{d-1}}"></span> par un point donné à travers une de ses faces. Il en résulte une division du polytope d'origine dans <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle R^{d-1}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msup>
<br/>          <mi>R</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>d</mi>
<br/>            <mo>−<!-- − --></mo>
<br/>            <mn>1</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle R^{d-1}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a1ace73ab45be2e58aaf709e7436c96ad4095ace" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:4.957ex; height:2.676ex;" alt="{\\\\displaystyle R^{d-1}}"></span> qui lui est combinatoirement équivalente.
<br/>Au début du <abbr class="abbr" title="20ᵉ siècle"><span class="romain">XX</span><sup style="font-size:72%">e</sup></abbr>&nbsp;siècle, les diagrammes de Schlegel s'avérèrent être des outils étonnamment pratiques pour l'étude des propriétés topologiques et combinatoires des polytopes. En dimension 3, un diagramme de Schlegel consiste en la projection d'un polyèdre sur une figure plane divisée en zones à l'intérieur (représentant les faces du polyèdre d'origine), et en dimension 4, il consiste en une projection d'un polychore dans un polyèdre divisé à l'intérieur en compartiments (représentant les cellules du polychore d'origine). Ainsi les diagrammes de Schlegel sont couramment employés dans le but de visualiser des objets quadridimensionnels.
<br/>C'est le mathématicien allemand Victor Schlegel (1843–1905) qui en a eu l'idée. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Diagramme_de_Schlegel">https://fr.wikipedia.org/wiki/Diagramme_de_Schlegel</a>)"""@fr, """In geometry, a <b>Schlegel diagram</b> is a projection of a polytope from <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\	extstyle \\\\mathbb {R} ^{d}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="false" scriptlevel="0">
<br/>        <msup>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="double-struck">R</mi>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>d</mi>
<br/>          </mrow>
<br/>        </msup>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\	extstyle \\\\mathbb {R} ^{d}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99e1d7aac444af9451aa84f7c95ad1561fdd1834" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:2.77ex; height:2.676ex;" alt="{\\	extstyle \\\\mathbb {R} ^{d}}"></span> into <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\	extstyle \\\\mathbb {R} ^{d-1}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="false" scriptlevel="0">
<br/>        <msup>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="double-struck">R</mi>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>d</mi>
<br/>            <mo>−<!-- − --></mo>
<br/>            <mn>1</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\	extstyle \\\\mathbb {R} ^{d-1}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6fc37e4ea461c049b9fe6991d0dbf137faa44e7" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:4.871ex; height:2.676ex;" alt="{\\	extstyle \\\\mathbb {R} ^{d-1}}"></span> through a point just outside one of its facets. The resulting entity is a polytopal subdivision of the facet in <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\	extstyle \\\\mathbb {R} ^{d-1}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="false" scriptlevel="0">
<br/>        <msup>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="double-struck">R</mi>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>d</mi>
<br/>            <mo>−<!-- − --></mo>
<br/>            <mn>1</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\	extstyle \\\\mathbb {R} ^{d-1}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6fc37e4ea461c049b9fe6991d0dbf137faa44e7" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:4.871ex; height:2.676ex;" alt="{\\	extstyle \\\\mathbb {R} ^{d-1}}"></span> that, together with the original facet, is combinatorially equivalent to the original polytope. The diagram is named for Victor Schlegel, who in 1886 introduced this tool for studying combinatorial and topological properties of polytopes. In dimension 3, a Schlegel diagram is a projection of a polyhedron into a plane figure; in dimension 4, it is a projection of a 4-polytope to 3-space. As such, Schlegel diagrams are commonly used as a means of visualizing four-dimensional polytopes. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Schlegel_diagram">https://en.wikipedia.org/wiki/Schlegel_diagram</a>)"""@en ;
  dc:modified "2023-07-28"^^xsd:date ;
  skos:prefLabel "diagramme de Schlegel"@fr, "Schlegel diagram"@en ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Schlegel_diagram>, <https://fr.wikipedia.org/wiki/Diagramme_de_Schlegel> ;
  a skos:Concept ;
  skos:inScheme psr: .

psr: a skos:ConceptScheme .
psr:-XPFQM0ZH-H
  skos:prefLabel "géométrie projective"@fr, "projective geometry"@en ;
  a skos:Concept ;
  skos:narrower psr:-LR1BQFJ7-F .

psr:-WVB8LP7M-L
  skos:prefLabel "polytope"@en, "polytope"@fr ;
  a skos:Concept ;
  skos:narrower psr:-LR1BQFJ7-F .