@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .

psr:-ZLZPWC0Z-9
  skos:prefLabel "nombre polyédrique"@fr, "polyhedral number"@en ;
  a skos:Concept ;
  skos:narrower psr:-L5F46MNK-R .

psr: a skos:ConceptScheme .
psr:-L5F46MNK-R
  skos:definition """Un <b>nombre dodécaédrique</b>&nbsp;est un nombre&nbsp;figuré&nbsp;polyédrique qui représente un dodécaèdre. Le nombre dodécaédrique pour un certain nombre&nbsp;<i>n</i> est donné par la formule&nbsp;:&nbsp;
<br/><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 {n(3n-1)(3n-2) \\\\over 2}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mrow>
<br/>              <mi>n</mi>
<br/>              <mo stretchy="false">(</mo>
<br/>              <mn>3</mn>
<br/>              <mi>n</mi>
<br/>              <mo>−<!-- − --></mo>
<br/>              <mn>1</mn>
<br/>              <mo stretchy="false">)</mo>
<br/>              <mo stretchy="false">(</mo>
<br/>              <mn>3</mn>
<br/>              <mi>n</mi>
<br/>              <mo>−<!-- − --></mo>
<br/>              <mn>2</mn>
<br/>              <mo stretchy="false">)</mo>
<br/>            </mrow>
<br/>            <mn>2</mn>
<br/>          </mfrac>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle {n(3n-1)(3n-2) \\\\over 2}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/acd68e068b25acdc21afd82cdec2b6b3214d5141" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.838ex; width:18.969ex; height:5.676ex;" alt="{\\\\displaystyle {n(3n-1)(3n-2) \\\\over 2}}"></span>
<br/>Les premiers de ces nombres sont 0, 1, 20, 84, 220, 455, 816, 1330, 2024, 2925, 4060, 5456, 7140, 9139, 11480, ... (séquence suite A006566 de l'OEIS).
<br/> 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Nombre_dod%C3%A9ca%C3%A9drique">https://fr.wikipedia.org/wiki/Nombre_dod%C3%A9ca%C3%A9drique</a>)"""@fr, """A <b>dodecahedral number</b> is a figurate number that represents a dodecahedron. The <i>n</i>th dodecahedral number is given by the formula
<br/><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 {n(3n-1)(3n-2) \\\\over 2}={3n \\\\choose 3}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mrow>
<br/>              <mi>n</mi>
<br/>              <mo stretchy="false">(</mo>
<br/>              <mn>3</mn>
<br/>              <mi>n</mi>
<br/>              <mo>−<!-- − --></mo>
<br/>              <mn>1</mn>
<br/>              <mo stretchy="false">)</mo>
<br/>              <mo stretchy="false">(</mo>
<br/>              <mn>3</mn>
<br/>              <mi>n</mi>
<br/>              <mo>−<!-- − --></mo>
<br/>              <mn>2</mn>
<br/>              <mo stretchy="false">)</mo>
<br/>            </mrow>
<br/>            <mn>2</mn>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mo>=</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mrow>
<br/>            <mrow class="MJX-TeXAtom-OPEN">
<br/>              <mo maxsize="2.047em" minsize="2.047em">(</mo>
<br/>            </mrow>
<br/>            <mfrac linethickness="0">
<br/>              <mrow>
<br/>                <mn>3</mn>
<br/>                <mi>n</mi>
<br/>              </mrow>
<br/>              <mn>3</mn>
<br/>            </mfrac>
<br/>            <mrow class="MJX-TeXAtom-CLOSE">
<br/>              <mo maxsize="2.047em" minsize="2.047em">)</mo>
<br/>            </mrow>
<br/>          </mrow>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle {n(3n-1)(3n-2) \\\\over 2}={3n \\\\choose 3}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/adef97e1a1a8674428f2db4d32288987df439398" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.505ex; width:28.046ex; height:6.343ex;" alt="{\\\\displaystyle {n(3n-1)(3n-2) \\\\over 2}={3n \\\\choose 3}}"></span>
<br/>The first such numbers are 0, 1, 20, 84, 220, 455, 816, 1330, 2024, 2925, 4060, 5456, 7140, 9139, 11480, … (sequence <span class="nowrap external">A006566</span> in the OEIS). 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Dodecahedral_number">https://en.wikipedia.org/wiki/Dodecahedral_number</a>)"""@en ;
  a skos:Concept ;
  skos:inScheme psr: ;
  skos:broader psr:-ZLZPWC0Z-9 ;
  skos:prefLabel "dodecahedral number"@en, "nombre dodécaédrique"@fr ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Nombre_dod%C3%A9ca%C3%A9drique>, <https://en.wikipedia.org/wiki/Dodecahedral_number> .