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Octant of a sphere
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<p>In <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, an octant of a sphere is a <a href="/facts/Spherical_triangle/3G3Fhk2h">spherical triangle</a> with three <a href="/facts/Right_angle/psaslRq7">right angles</a> and three right sides. It is sometimes called a trirectangular (spherical) triangle. It is one face of a <a href="/facts/Spherical_octahedron/G38q92xW">spherical octahedron</a>. </p><p>For a <a href="/facts/Sphere/jywYLNM2">sphere</a> embedded in <a href="/facts/Three-dimensional_Euclidean_space/KAqKWUbS">three-dimensional Euclidean space</a>, the <a href="/facts/Euclidean_vector/bCLrdksy">vectors</a> from the sphere's center to each vertex of an octant are the <a href="/facts/Basis_vector/89IPoN6c">basis vectors</a> of a <a href="/facts/Cartesian_coordinate_system/lkTqvMmB">Cartesian coordinate system</a> relative to which the sphere is a <a href="/facts/Unit_sphere/5UeoTcug">unit sphere</a>. The spherical octant itself is the intersection of the sphere with one <a href="/facts/Octant_(solid_geometry)/r1j1h9mz">octant of space</a>. </p><p>Uniquely among spherical triangles, the octant is its own <a href="/facts/Polar_triangle/3G3Fhk2h">polar triangle</a>. </p><p>The octant can be parametrized using a rational quartic <a href="/facts/B%25C3%25A9zier_triangle/uu8EDGo1">Bézier triangle</a>. </p><p>The <a href="/facts/Solid_angle/se8IXufg">solid angle</a> subtended by a spherical octant is π/2 <a href="/facts/Steradian/PRCqT4n1">steradian</a> or one-eight of a <a href="/facts/Spat_(angular_unit)/oMz4w8rI">spat</a>, the solid angle of a full sphere. </p>