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7-simplex
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<table><tbody><tr><th colspan="2">Regular octaexon(7-simplex)</th></tr><tr><td colspan="2"><a href="/facts/Orthogonal_projection/sElXGkxD">Orthogonal projection</a>inside <a href="/facts/Petrie_polygon/uDmot1hD">Petrie polygon</a></td></tr><tr><td>Type</td><td>Regular <a href="/facts/7-polytope/suCJSvTN">7-polytope</a></td></tr><tr><td>Family</td><td><a href="/facts/Simplex/0FCfNRN8">simplex</a></td></tr><tr><td><a href="/facts/Schl%25C3%25A4fli_symbol/jNQR77UU">Schläfli symbol</a></td><td>{3,3,3,3,3,3}</td></tr><tr><td><a href="/facts/Coxeter-Dynkin_diagram/Ik6LmXJB">Coxeter-Dynkin diagram</a></td><td></td></tr><tr><td>6-faces</td><td>8 <a href="/facts/6-simplex/mInfSIeH">6-simplex</a></td></tr><tr><td>5-faces</td><td>28 <a href="/facts/5-simplex/KIfBFfhl">5-simplex</a></td></tr><tr><td>4-faces</td><td>56 <a href="/facts/5-cell/Rh6lwDcc">5-cell</a></td></tr><tr><td>Cells</td><td>70 <a href="/facts/Tetrahedron/7mkSrl6j">tetrahedron</a></td></tr><tr><td>Faces</td><td>56 <a href="/facts/Triangle/cRXUwsMn">triangle</a></td></tr><tr><td>Edges</td><td>28</td></tr><tr><td>Vertices</td><td>8</td></tr><tr><td><a href="/facts/Vertex_figure/3u2ySK0C">Vertex figure</a></td><td><a href="/facts/6-simplex/mInfSIeH">6-simplex</a></td></tr><tr><td><a href="/facts/Petrie_polygon/uDmot1hD">Petrie polygon</a></td><td><a href="/facts/Octagon/H5PuP3wP">octagon</a></td></tr><tr><td><a href="/facts/Coxeter_group/bgzHFm1Q">Coxeter group</a></td><td>A7 [3,3,3,3,3,3]</td></tr><tr><td>Dual</td><td><a href="/facts/Self-dual_polytope/rkIHbmAf">Self-dual</a></td></tr><tr><td>Properties</td><td><a href="/facts/Convex_polytope/2pRHcRgC">convex</a></td></tr></tbody></table> <p>In <a href="/facts/Seven-dimensional_space/Cw6WuFgL">7-dimensional</a> <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, a 7-<a href="/facts/Simplex/0FCfNRN8">simplex</a> is a self-dual <a href="/facts/Regular_polytope/RYTnEF6Q">regular</a> <a href="/facts/7-polytope/suCJSvTN">7-polytope</a>. It has 8 <a href="/facts/Vertex_(geometry)/ID3cea9z">vertices</a>, 28 <a href="/facts/Edge_(geometry)/3lFN6sEz">edges</a>, 56 triangle <a href="/facts/Face_(geometry)/T2E6BTU4">faces</a>, 70 tetrahedral <a href="/facts/Cell_(mathematics)/T2E6BTU4">cells</a>, 56 <a href="/facts/5-cell/Rh6lwDcc">5-cell</a> 5-faces, 28 <a href="/facts/5-simplex/KIfBFfhl">5-simplex</a> 6-faces, and 8 <a href="/facts/6-simplex/mInfSIeH">6-simplex</a> 7-faces. Its <a href="/facts/Dihedral_angle/C9WEJsuS">dihedral angle</a> is cos−1(1/7), or approximately 81.79°. </p>