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Kepler–Poinsot polyhedron
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=== Summary === {| class="wikitable" |- !Name<br>(Conway's abbreviation) !Picture !Spherical<BR>tiling ![[Stellation]]<BR>diagram ![[Schläfli symbol|Schläfli]]<br />{p, q} and<br />[[Coxeter-Dynkin diagram|Coxeter-Dynkin]] !Faces<br />{p} !Edges !Vertices<br />{q} ![[Vertex figure|Vertex<BR>figure]]<BR>[[Vertex configuration|(config.)]] ![[Petrie polygon]] ![[Euler characteristic|χ]] ![[Density (polytope)|Density]] ![[Symmetry group|Symmetry]] ![[dual polyhedron|Dual]] |- align=center |[[great dodecahedron]]<br>(gD) |[[Image:Great dodecahedron (gray with yellow face).svg|80px]] |[[Image:Great dodecahedron tiling.svg|80px]] |[[File:Second stellation of dodecahedron facets.svg|80px]] |{5, 5/2}<br />{{CDD|node_1|5|node|5|rat|d2|node}} |12<br />{5} |30||12<br />{5/2}||[[File:Great dodecahedron vertfig.png|80px]]<BR>(5<sup>5</sup>)/2 |[[File:Skeleton Gr12, Petrie, stick, size m, 3-fold.png|80px]]<br>{6} | −6||3||I<sub>h</sub>||small stellated dodecahedron |- align=center |[[small stellated dodecahedron]]<br>(sD) |[[Image:Small stellated dodecahedron (gray with yellow face).svg|80px]] |[[Image:Small stellated dodecahedron tiling.png|80px]] |[[File:First stellation of dodecahedron facets.svg|80px]] |{5/2, 5}<br />{{CDD|node|5|node|5|rat|d2|node_1}} |12<br />{5/2} |30||12<br />{5}||[[File:Small stellated dodecahedron vertfig.png|80px]]<BR>(5/2)<sup>5</sup> |[[File:Skeleton St12, Petrie, stick, size m, 3-fold.png|80px]]<br>{6} | −6||3||I<sub>h</sub>||great dodecahedron |- align=center |[[great icosahedron]]<br>(gI) |[[Image:Great icosahedron (gray with yellow face).svg|80px]] |[[Image:Great icosahedron tiling.svg|80px]] |[[File:Great icosahedron stellation facets.svg|80px]] |{3, 5/2}<br />{{CDD|node_1|3|node|5|rat|d2|node}} |20<br />{3} |30||12<br />{5/2}||[[File:Great icosahedron vertfig.svg|80px]]<BR>(3<sup>5</sup>)/2 |[[File:Skeleton Gr20, Petrie, stick, size m, 5-fold.png|80px]]<br>{10/3} |2||7||I<sub>h</sub>||great stellated dodecahedron |- align=center |[[great stellated dodecahedron]]<br>(sgD = gsD) |[[Image:Great stellated dodecahedron (gray with yellow face).svg|80px]] |[[Image:Great stellated dodecahedron tiling.svg|80px]] |[[File:Third stellation of dodecahedron facets.svg|80px]] |{5/2, 3}<br />{{CDD|node|3|node|5|rat|d2|node_1}} |12<br />{5/2} |30||20<br />{3}||[[File:Great stellated dodecahedron vertfig.png|80px]]<BR>(5/2)<sup>3</sup> |[[File:Skeleton GrSt12, Petrie, stick, size m, 5-fold.png|80px]]<br>{10/3} |2||7||I<sub>h</sub>||great icosahedron |}
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