@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:-KM9J4J44-Q .

psr:-KM9J4J44-Q
  skos:definition """Un <b>nombre icosaédrique</b> est un nombre figuré&nbsp;polyédrique qui représente un icosaèdre. Le nombre icosaédrique pour un certain nombre&nbsp;<i>n</i> est donné par la formule&nbsp;:&nbsp;
<br/>
<br/><dl><dd><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(5n^{2}-5n+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>5</mn>
<br/>              <msup>
<br/>                <mi>n</mi>
<br/>                <mrow class="MJX-TeXAtom-ORD">
<br/>                  <mn>2</mn>
<br/>                </mrow>
<br/>              </msup>
<br/>              <mo>−<!-- − --></mo>
<br/>              <mn>5</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(5n^{2}-5n+2) \\\\over 2}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb2acf163539418f1afeae275774c75dc85c4e90" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.838ex; width:17.052ex; height:5.843ex;" alt="{\\\\displaystyle {n(5n^{2}-5n+2) \\\\over 2}}"></span></dd></dl>
<br/>Les premiers de ces nombres sont 1, 12, 48, 124, 255, 456, 742, 1128, 1629, 2260, 3036, 3972, 5083, ... (séquence suite A006564 de l'OEIS). 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Nombre_icosa%C3%A9drique">https://fr.wikipedia.org/wiki/Nombre_icosa%C3%A9drique</a>)"""@fr, """An <b>icosahedral number</b> is a figurate number that represents an icosahedron. The <i>n</i>th icosahedral number is given by the formula
<br/>
<br/><dl><dd><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(5n^{2}-5n+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>5</mn>
<br/>              <msup>
<br/>                <mi>n</mi>
<br/>                <mrow class="MJX-TeXAtom-ORD">
<br/>                  <mn>2</mn>
<br/>                </mrow>
<br/>              </msup>
<br/>              <mo>−<!-- − --></mo>
<br/>              <mn>5</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(5n^{2}-5n+2) \\\\over 2}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb2acf163539418f1afeae275774c75dc85c4e90" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.838ex; width:17.052ex; height:5.843ex;" alt="{\\\\displaystyle {n(5n^{2}-5n+2) \\\\over 2}}"></span></dd></dl>
<br/>The first such numbers are 1, 12, 48, 124, 255, 456, 742, 1128, 1629, 2260, 3036, 3972, 5083, … (sequence A006564 in the OEIS). 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Icosahedral_number">https://en.wikipedia.org/wiki/Icosahedral_number</a>)"""@en ;
  a skos:Concept ;
  skos:inScheme psr: ;
  skos:broader psr:-ZLZPWC0Z-9 ;
  skos:prefLabel "icosahedral number"@en, "nombre icosaédrique"@fr ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Nombre_icosa%C3%A9drique>, <https://en.wikipedia.org/wiki/Icosahedral_number> .

psr: a skos:ConceptScheme .