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List of regular polytopes
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Example regular polytopes<table><tbody><tr><th colspan="2">Regular (2D) polygons</th></tr><tr><th>Convex</th><th>Star</th></tr><tr><td><a href="/facts/Pentagon/jeHEARHH">{5}</a></td><td><a href="/facts/Pentagram/cN0ke8tp">{5/2}</a></td></tr><tr><th colspan="2">Regular (3D) polyhedra</th></tr><tr><th>Convex</th><th>Star</th></tr><tr><td><a href="/facts/Dodecahedron/7r519eCl">{5,3}</a></td><td><a href="/facts/Small_stellated_dodecahedron/lX1zlo6C">{5/2,5}</a></td></tr><tr><th colspan="2">Regular 4D polytopes</th></tr><tr><th>Convex</th><th>Star</th></tr><tr><td><a href="/facts/120-cell/W4nroBjJ">{5,3,3}</a></td><td><a href="/facts/Small_stellated_120-cell/v58V84tU">{5/2,5,3}</a></td></tr><tr><th colspan="2">Regular 2D tessellations</th></tr><tr><th>Euclidean</th><th>Hyperbolic</th></tr><tr><td><a href="/facts/Square_tiling/3ym86mvv">{4,4}</a></td><td><a href="/facts/Order-4_pentagonal_tiling/aHah4SUB">{5,4}</a></td></tr><tr><th colspan="2">Regular 3D tessellations</th></tr><tr><th>Euclidean</th><th>Hyperbolic</th></tr><tr><td><a href="/facts/Cubic_honeycomb/eMxySFur">{4,3,4}</a></td><td><a href="/facts/Order-4_dodecahedral_honeycomb/7o9f0LoA">{5,3,4}</a></td></tr></tbody></table> <p>This article lists the <a href="/facts/Regular_polytope/RYTnEF6Q">regular polytopes</a> in <a href="/facts/Euclidean_geometry/V6cTcoCy">Euclidean</a>, <a href="/facts/Spherical_geometry/WGLQb1Ys">spherical</a> and <a href="/facts/Hyperbolic_geometry/DjTMKdgy">hyperbolic</a> spaces. </p>