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Compound of four octahedra
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<table><tbody><tr><th colspan="2">Compound of four octahedra</th></tr><tr><td colspan="2"></td></tr><tr><td>Type</td><td><a href="/facts/Uniform_polyhedron_compound/NxW4PHo5">Uniform compound</a></td></tr><tr><td>Index</td><td>UC12</td></tr><tr><td><a href="/facts/Convex_hull/D4Id3JDS">Convex hull</a></td><td>Nonuniform <a href="/facts/Truncated_cube/XVAUG4fD">truncated cube</a></td></tr><tr><td>Polyhedra</td><td>4 <a href="/facts/Octahedron/G38q92xW">octahedra</a></td></tr><tr><td>Faces</td><td>8+24 <a href="/facts/Triangles/cRXUwsMn">triangles</a></td></tr><tr><td>Edges</td><td>48</td></tr><tr><td>Vertices</td><td>24</td></tr><tr><td><a href="/facts/List_of_spherical_symmetry_groups/3X3YcHoQ">Symmetry group</a></td><td><a href="/facts/Octahedral_symmetry/qLqhYxgm">octahedral</a> (<i>O</i>h)</td></tr><tr><td><a href="/facts/Subgroup/r91mBgpa">Subgroup</a> restricting to one constituent</td><td>3-fold <a href="/facts/Dihedral_symmetry_in_three_dimensions/xNRpsIAF">antiprismatic</a> (<i>D</i>3d)</td></tr></tbody></table> <p>The compound of four octahedra is a <a href="/facts/Uniform_polyhedron_compound/NxW4PHo5">uniform polyhedron compound</a>. It's composed of a symmetric arrangement of 4 <a href="/facts/Octahedron/G38q92xW">octahedra</a>, considered as triangular <a href="/facts/Antiprisms/FgP5jIVd">antiprisms</a>. It can be constructed by superimposing four identical octahedra, and then rotating each by 60 degrees about a separate axis (that passes through the centres of two opposite octahedral faces). </p><p>Its dual is the <a href="/facts/Compound_of_four_cubes/6nLLEEQB">compound of four cubes</a>. </p>